2 HALF-LIFE AND MEAN LIFE It is a common practice to use the half-life (T1/2) instead of the decay constant ( ) for indicating the degree of instability or the decay rate of a radioactive nuclide. Half-life is the amount of time elapsed for the isotope amount to reduce by half when it goes through radioactive, or nuclear decay. So for the first half-life, the first half-life is say time would be 5 seconds. Nuclear Half-Life - Chemistry | Socratic nuclear chemistry half life answers Blm Grade 8 Answers, romeo and juliet study guide questions answers, Forensic Science A To Z Challenge Answers, milady chapter 11 test answers, Answers To Prentice Hall Literature Book, Nuclear Chemistry Half Life Answers - kids. Calculate the half-life for the hydrolysis reaction under these conditions. Consider the following example. Definition of half-life. If a sample initially contains 5. If the half-life is too short, it may require more frequent dosing in order to maintain desired exposures and avoid unnecessarily high peak concentrations. The Half-Life Calculator is used to calculate the half-life in exponential decay. 5 grams in 21. Because half life computations may be either probabilistic or deterministic it is important to consider the difference between each method since each method is used extensively in nuclear physics, chemistry, and medicine as well as in commerce, business and finance. For a first order reaction, t½ = 0. One of the most well-known applications of half-life is carbon-14 dating. Ke (Elimination Rate) -- Half-Life. The clearance is 0. rays converts bitrogen to a radioactive isotope of carbon, C-14, with a half . 0 gram sample is 3 years, This free half-life calculator can determine any of the values in the half-life formula given three of the four values. This phenomenon takes place every day in many chemical reactions and nuclear reactions, and it is called the half-life, which is the amount of time it takes for half of a sample to react. 2014. Uranium-238 has a very long half life of 4. g seconds, minutes, days, years, millions of years!) since half-life=ln2/ λ , and average or mean-life=1/ λ hence avg-life=half-life/ln2=1. jdrf. 46 . (i) If half life period of first order reaction is x and 3/4 th life period of same reaction is ’y’, how are V and ’y’ related to each other? (ii) In some cases it is found that a large number of colliding molecules have energy more than threshold energy but yet the reaction is slow. Half-Life of an Element. 4 hours. 9 minutes. Calculate the decay constant (k). Calculate the age of a material based upon its half-life. 25 g 15. The doubling time of a population exhibiting exponential growth is the time required for a population to double. Interestingly enough, the half-life of a compound undergoing a decomposition reaction (or any first-order chemical reaction) is calculated in exactly the same way, except A is the concentration of the compound instead of the activity of the radionuclide. The number of decay is not completely The study of chemical kinetics is the study of change over time. And you're going to learn to employ the concept of half-life and see the relationship between a rate constant and the value for half-life, and be able to utilize those into calculations. 00g sample of Au-l 98 to decay to 6. By selecting an element from the table below, you are specifying the half life that appears in Half-life is the time it takes for half of the original sample of radioactive nuclei to decay. (Once decayed, they are now “safe” to eat. This Half-Life Problems Worksheet is suitable for 9th - 12th Grade. Note that the radioactive half-life is not the same as the average lifetime, the half-life being 0. Kilogramms, Milligramms, %, etc. Definition. A useful application of half-lives is radioactive dating. The term has transmutated, scientist can calculate and estimate the age of a substance. Description: With the Half-Life Laboratory, students gain a better understanding of radioactive dating and half-lives. Nuclear waste being buried at a special site. Last updated Chemosphere. (2) Using half-life data in hazard analysis and more on prediction of radioisotope residue. If a 30. The hormone half-life is used in the deconvolution analysis to calculate the secretion rate of a given hormone, and usually is not known precisely, but rather is estimated from population physiology studies. The half life is the time for half the nuclei to decay. 4 days when the dose is 0. Radioactive decay is a constant process where the unstable radioactive element breaks down to become a more stable element by releasing radioactive particles and radiation. Now we're gonna talk about the concept of half-life. The half-life is the amount of time taken for one half of the initial reactants to be used up. besides the indisputable fact that, you dont favor this, in case you in simple terms have finished 1/2-life cases. concentration of the radioactive nuclide, we will calculate the specific tritium (3H) . . (b) Calculate the rate constant, k, for the reaction at 350. 41 multiplied by 104 years. Suppose we have 100 nuclei of a radioactive isotope. 49 seconds, 1. However this can be automatically converted to compatible How to calculate half-life (chemistry)? 239Pu is a radioactive element used in atomic weapons and some nuclear reactors. 2. 00 g of fluorine-20, how much remains after 44. After five half-life periods for a first order reaction, what fraction of reactant remains? 4. The isotope Uranium-238 has a half life as long as 4. If a freshly prepared solution of cisplatin has a concentration of 0. Get the free "Half Life Calculator (second order reaction)" widget for your website, blog, Wordpress, Blogger, or iGoogle. A radioactive isotope of element decays with a half-life of 10. The mathematical equation that describes this process is: ; where N is the activity with the actual value given by the HANDBOOK OF CHEMISTRY AND PHYSICS. 2 The pupils copy the ‘half-life duration’ for the first five half-lives from the onscreen table into their worksheet tables and calculate the average half-life. Instead of trying to identify the time required for the reaction to become completed, it is far more practical to specify the the time required for the concentration of a reactant to fall to half of its initial value. Although chemical changes were sped up or slowed down by changing factors such This video explains half-life in the context of radioactive decay. 0 s is exactly 4 half-lives, so using the previous expression, n = 4. How many half-lives will pass by the time a 60. 3. Now let's think about this. potassium-40 half life = 1. Half-life As defined by geophysicists, the half-life (or half-value period) of a substance is On the other hand, the speeds of many chemical reactions depend on the The mathematical equation which describes how the number of atoms, and 1, The Determination of a Chemical Formula 33, Determining the Half-Life of an Isotope. 5 billion years whereas the half life of Thorium-234 is as little as 24 days. Carbon dating is a method of determining the age of an object using the properties of radiocarbon. The process and formula for calculating half-life is the same, regardless of whether it is a psychotropic or other medicine. Recall that a first-order process has a characteristic half-life, which is the time required for half of any given quantity of a substance to react. 75 g have decayed Note that the length of the half-life played no role in this calculation. 25 x 10 4 years. is the time required for half of the atoms of a radioactive isotope to undergo decay. Another concept that is important to understand with respect to reaction rate is the half-life. For three or more processes, the analogous formula is: In a chemical reaction, the half-life of a species is the time it takes for the concentration of that Sep 9, 2019 Calculate the age of a material based upon its half-life. Experiments have shown that the rate of a 5. so terminal halflife here is 28 days $\endgroup$ – Roger Johansson Jul 15 A sample of $\ce{^{41}Ar}$, a radioisotope used to measure the flow of gases from smokestacks, decays initially at a rate of 34,500 disintegrations/min, but the decay rate falls to 21,500 disintegr The half-life of fluorine-20 is 11. Estimate the half-life, t 1/2, of the single unknown average. Calculate the half-life. Brown, H. 0 g - 1. The activity of a radioactive substance is defined as the average number of atoms disintegrating per unit time. Students are able to visualize and model what is meant by the half-life of a reaction. Doubling time. A clinical study carried out among 52 volunteers showed that THC-COOH was detectable in serum from 3. The half-life of a specific radioactive isotope is constant; it is unaffected by conditions and is independent of the initial amount of that isotope. But im having . You can use the half life equation to calculate how long radioactive waste will remain dangerous. If you are given two count rates and you An interesting and useful aspect of radioactive decay is half-life, which is the amount of time it takes for one-half of a radioactive isotope to decay. In our last lesson we talked about the integrative rate law for first-order kinetics. Half-life is the amount of time required for half of a quantity of a radioactive element to decay. Half life. Remember, half-life of a radioisotope is defined as the time it takes for half the isotope to undergo nuclear decay. 2 s after the reaction starts. (b) What is the value of the half-life of the reaction? (c) How long will it take for the reaction to go to 95. Give your answer in becquerels and in curies. radon-224 half life = 55 seconds) to millions of years (e. This can set up a good discussion of what is happening to the number of students still standing (i. Chemistry Regents Reference Tables to assist you in answering the following questions. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo, or how long stable atoms survive, radioactive decay. g. Describe how carbon-14 is used to determine the age of carbon containing objects. When the pressure was 28. 0 gram sample is 3 years, then in 3 years only 25 grams would remain. The example that causes the most confusion is the decay of the free neutron with a half-life of 10. And so your half-life is constant. If your calculator doesn't have a percentage button, you multiply the whole value by 0. Category Describe what is meant by the term half-life and what factors affect half-life. The Half Life Time is the amount of time it takes for half of the atoms in a sample to decay. For a given reaction the half life t1/2 of a reactant is the time required for its concentration to reach a value that is the arithmetic mean of its initial and final (equilibrium) value. Calculate the mass of Cs-137 that will be left after 90 years. Half Life Chemistry Examples The half-life of a reaction is the amount of time it takes for the concentration of a Consider, for example, a first-order reaction that has a rate constant of 5. ** This is the number of half lives that have passed. Record the number of “radioactive” atoms remaining. After a certain period of time the value of (N₀/N ) becomes one half, that is, half of the radioactive elements have undergone disintegration. of instability which, as we will see, is going to be expressed by the half-life . 1. pdf. of C-14 begins to decrease through radioactive decay. This is the 2nd half life. 2. 0 mol dm-3 is called the half-life. The most obvious instance is drugs; the half-life is the time it takes for their effect to halve, or for half of the substance to leave the body. 0173 M 41. Calculate the time required for 90% completion of this reaction. Hence, the number of half-lives is 4. It's necessary to have discussed half-life at both a conceptual level and a mathematical level before Half life of a reaction is defined as the time required for reducing the concentration of a reactant to half its initial value. You have 8g of starting material. The term half-life is defined as the time it takes for one-half of the atoms of a radioactive material to disintegrate. www. 0 gram sample would have decayed after exactly three half-lives? Solution: (1/2) 3 = 0. 40*10-2 and after 50 years only 25 mg remain, calculate the amount originally present. SaralStudy helps in prepare for NCERT CBSE solutions for Class 12th chemistry. 0 y. } 1 How long does it take a 100. Notes on General Chemistry http://quantum. This time is called the half-life, and often denoted by the symbol t 1/2. Click on Calculate Time or Calculate Half-time or Calculate Beginning The Half Life Time is the amount of time it takes for half of the atoms in a sample to decay. In ALL cases, you can use the rate law to calculate the expression for half-life. Radioactive Decay and Half-Life. It is used in the nuclear physics to undergo the stability of the atoms, that is radioactive decay. The calculations video for this portion of the notes is at the bottom of the page. Half-Life Practice Problems . 8~min = 26. 00 s -1. 693 t k Part 3. Real-life chemists in real-life labs don’t make every solution from scratch. Be sure to use correct sig figs in your responses. This is the reverse of the radioactive decay calculations. The patient weighs 70 kg. You can use it to not only learn how to calculate half life, but also as a way of finding the initial and final quantity of a substance or its decay constant. 0709 M 60. A half-life of 12–48 h is generally ideal for once daily dosing of oral drugs. 25 g remain 10. Some isotopes are very stable, undergo decay very slowly, and have extremely long half-lives. AND, you might be given an equation sheet that has these expressions on it. Unterweger, D. Implicit in this definition is the fact that, no matter when you start measuring, the population will always take the same amount of time to double. Radioactive Half-Life and Decay(Retrieved Dec. Or, it may be defined as the time for the radioactivity of an isotope to be reduced to half of its original value. Use this decay calculator to easily calculate the time elapsed since the beginning of the decay, or calculate the original quantity, half-life or remaining quantity of a substance subject to radioactive decay, based on any of the three parameters. 0μg, calculate the number of days it will take for the radioactive isotope to drop to 1. 1/2 0. The half-life of a substance undergoing decay is the time it takes for the amount of the substance to decrease by half. Half-life: Calculating Radioactive Decay and Interpreting Decay Graphs . It has a half-life of 6. Place the atoms that didn’t decay (candies with “m” facing up) back into the cup and shake for another 10-sec time interval. 04 mg/kg of body weight, 13. How do i solve Half life (problem) - The half-life od radium-222 is 38 seconds. To make a dilution, you simply add a small quantity of a concentrated stock solution to an amount of pure solvent. 5 hours. How much will you have 20 hours from now? Please show how to work. 50μg. 5 g 31. As discussed before, the t 1 / 2 of a zero order reaction is given as. org Nuclear Chemistry : Half-Life Quiz. A discarded oyster shell from someone's dinner eaten 11,460 years ago (two half lives) would have one quarter the 14 C: 12 C ratio that a cotton shirt worn today would. . If we compare the time that has passed to the isotope’s half-life, we note that 44. minutes. Substituting and solving results in the following: Half-life is th© time required for one-half of a radioactive nuclide to decay (change to another element), it Is possible to'calculate the amount of a radioactive element that will be left If we know its half-life. The half- life of it for an infrequent user is 1. Instead, they make concentrated stock solutions and then make dilutions of those stocks as necessary for a given experiment. The half-life is the length of time required for half of any given amount of an element to decay into another element. I-131, used in thyroid scans, has a half-life of 8. Follow Us Home >> Text Solution >> Chemical Kinetics >> calculate the half life of a first order reaction SaralStudy helps in prepare for NCERT CBSE solutions for Class 12th chemistry. 00 mg = 18. Balancing Redox Reactions: Redox equations are often so complex that fiddling with coefficients to balance chemical equations. Schima (1992), is a revised listing of the half lives determined at NIST since 1967 the half-life of the substance in question, any times that are given . 9 when the dose is 1 mg/kg Use this calculator to investigate how a unstable substance decays over time. Half-life (symbol t 1⁄2) is the time required for a quantity to reduce to half of its initial value. How many grams of radium-222 remian in a 12 gram sample after 152 Seconds? After 228 seconds? HW Q 15. 4~min}$. A half-life is the period of time it takes for a substance undergoing decay to decrease by half. Chemistry: The Central Science, Eleventh Edition By Theodore E. If k is a constant, obviously . The Beta decay equation of 90 Sr is given as: 38 90 Sr → 39 90 Y + -1 0 e. INSTRUCTIONS: Enter the following: (k) This is the temperature dependent reaction rate constant. 3 x 10 9 years). 443*half-life Get the free "Half Life Calculator (first order reaction)" widget for your website, blog, Wordpress, Blogger, or iGoogle. Carbon-14 has a half-life of 5730 years. 5 h. For example, the half-life of a chemical someone ingests might depend on the Calculating this time is important for establishing how frequently a message Apr 8, 2012 How do you calculate the radioactive half-life? Radioactive half-life can be used to describe how old something is by measuring how much of a Therefore, over one half-life of a chemical, one half of it will disappear. J. D. Contents of this slide-share presentation: Understanding decay concepts Facts about Radioactive decay Types of radioactive decay Understanding Half-life concep… Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. 3 hours. 5 g remains, and so on. after one half-life, 1 / 2 is left, after two half-lives, 1 / 4 is left, after three half-lives, 1 / 8 is left in other words its a 'halving pattern' etc. calculation uses the effective half-life; in radiation dosimetry calculations, the Half-Life Calculator, exponential decay, Radioactivity. Epub 2014 Aug 20. After 30 days, 25 g will remain, and after 45 days, 12. 1 s after the reaction starts. Unit Converter Convert length, temperature, speed and area measurements between different units. What is the half-life of argon-35? 8. Half-life period of radioactive elements. All 10 grams were carbon. Depending on the isotope, its Half Life may range from a few fractions of a second to several billion years. For example, if one begins with a gram of carbon-10, 20 seconds later only half a gram will remain, after 40 seconds only a quarter gram will be left, after 60 seconds an eighth of a gram, after 80 seconds one sixteenth of a gram, and after 100 seconds have elapsed from the Uranium-238 nucleus. This period is called half-life of a radioactive element and is a characteristic property of a radioactive element. 061. The animation below explains the half life of a radioactive isotope. During the next 3 years, 12. 393 g in 10. To answer this question The half life of the reaction, t ½. BYJU’S half-life calculator tool is easy to access. The ln(2) stands for the natural logarithm of two and can be estimated as 0. The Half Life of Uranium-235 is 713,000,000 years. chemosphere. Calculate the rate constant for the decay of . The half-life of tin in the liver and kidneys has been estimated as 3–4 days after oral absorption of diethyltin chloride in rats, but is longer in muscles and bone. Inputting two activities at two different dates and/or times, the half life may be calculated. Half-life and decay are important concepts in Chemistry. 25g? 2. The half-life for radioactive decay of 14 C is 5730 years. I know the forward and reverse rate constants. HALF-LIFE CALCULATIONS Nam© Half-life Is th© time required for one-half of a radioactive nuclide to decay (change to another element). Question 2 If you start with a 1. Original and resultung amount have the same value (e. [Physics FAQ] - Original May 2003 by Don Koks. A hospital laboratory has 80. Calculate the half-life , t1/2 using equation (7), for 20 F from each of the six replicate channel A runs and enter your result below. OR the time for the rate of decay to halve. 693 times the average lifetime. write an introduction for a lab report. For any particular radioisotope the count rate and time will be different but the shape of the curve will be the same. The device identified 126 of these events in one year, enabling researchers to calculate the isotope’s half-life. You look up the half life and then you know in how many hours, days, or weeks it takes for that isotope to get to that half life. asked by Sarah on October 24, 2013; Chemistry. The half-life can be written in terms of the decay constant, or the mean lifetime, as: Definition for Half-Life :The time it takes for one-half of the atoms of an unstable element or nuclide to decay radioactively into another element or nuclide. Step 2: Determine how many times the quantity of sample will be halved in 90 years. 7 days. Bursten, and Catherine J. Strontium-90 Beta Decay Equation. The Vd is 50L/kg. From the half-life you can calculate how much of the radio-active atoms are left e. The easiest way to measure the half-life from the graph is to. mi = the initial or half life problems and solutions radioactivity is decreased, find half life radioactive half life example graphs decay to zero chemistry radioactivity in solution + T1/2 half life and radioactive decay chemistry tutorials radioactive decay finding initial mass The rate of nuclear decay does not depend on temperature true or false M&M’s, Pennies, Puzzle Pieces & Licorice With the Half-Life Laboratory, students gain a better understanding of radioactive dating and half-lives. When a plant or animal dies it stops replacing its carbon and the amount . By First Order Kinetics -- Half-Life ? (a) Calculate the rate constant (with appropriate units) for a first order reaction which is 19. 625 g 7. Each isotope has its own characteristic half-life. billion. Half-life Calculator - Exponential decay Below we have a half-life calculator. Uranium-238 Half Lif. But, since this is a first order reaction, then [A] does factor into the half life and thus the time to reach $\mathrm{50~mmHg}$ should be slightly higher than $\mathrm{26. - Start here once you have a good idea of what half-life is. 5 kPa was 340s. Half life means that after that amount of time, the initial value will decrease by half. Half-life, or t½, is the time that elapses before the concentration of a reactant is reduced to half its initial Problem #3: Os-182 has a half-life of 21. The rate at which a radioactive isotope decays is measured in half-life. An activity of one decay per second is one Half-life, in radioactivity, the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay (change spontaneously into other nuclear species by emitting particles and energy), or, equivalently, the time interval required for the number of disintegrations per Calculate the half-life for the antibiotic. 7 x 10 24 years! Time-saving video on half-life. So how can you learn everything about chemistry without effort? We don’t know the answer, but we can help you solve chemistry problems faster and more efficiently thanks to our chemistry calculators. 468 billon years. What are Half Lives and Mean Lives? Specifying the half life or mean life of a process is a way of quantifying how fast it is occurring, when the whole process would in principle take forever to complete. 75 g. r Example: The half-life of Po^M Is 0. 005, which is the numerical value of half a percent. Second order reactions are dependent on concentration, just like first order reactions; however, second order reactions react much faster than first order. Here, the -1 0 e denotes a negative (-ve) beta particle or an electron. You may also back decay sources to find out the original activity (or for any date), knowing the current activity. 2 mg/kg and 14. Drug half-life has important implications for dosing regimen and peak-to-trough ratio at the steady state. Potassium-42 has a half-life of 12. For your convenience, the medicine half life calculator provides a series of measurement units and the result will respect the unit selection. Bismuth-209 is a stable radioactive isotope that undergoes alpha-decay, but has a half-life of 1. It's like cutting a cookie in half. Other isotopes have shorter half-lives. 4. The relationship between time, half-life, and the amount of radionuclide is defined by: [latex]N={N}_{0}{e}^{-\lambda t}[/latex] . I got 25. I note that the t-chart should have time in multiples of the half-life, and the mass dividing in half at each half-life. - Estimate the amount of radioactive substance based on the half-life. So we started with this. For exponential decay, we can define a characteristic half-life. Top. The half-life of Carbon-14 is 5700 years. Probabilistic and Deterministic Computations []. button. glencoe. In biology, a half-life is the time taken for a substance to lose half its effects. In this decay model, the green squares represent the parent unstable nuclei Calculate the oxidation numbers of the atoms or ions involved in a chemical reaction using the oxidation number rules. The half life of a specific element was calculated to be 5200 yr. 5 followed by the % button. If a reactant is used up according to a first order rate equation, and the initial concentration of the reactant is 3. In this equation, T1/2 is the half-life. Calculation of chemical elimination half-life from blood with Nov 8, 2016 Jump down to: Isotopes | Half-life | Isotope systems | Carbon-14 shares the same atomic number and chemical properties (and so occupies the by measuring the relative abundance of radioactive and radiogenic isotopes. 0 h. The radioactive half-life for a given radioisotope is a measure of the tendency of the nucleus to "decay" or "disintegrate" and as such is based purely upon that probability. It was originally used to describe the decay of radioactive elements like uranium or The half-life of a reaction, t1/2, is the amount of time needed for a reactant concentration to decrease by half compared to its initial concentration. 26x109 For a first-order reaction, the half-life is independent of reactant concentration (or pressure) at constant . Calculate the age of the wood, in years. Half-Life The half-life of a radioactive substance is a characteristic constant. BUT, if you're not strong with math, it might seem challenging. We can apply our knowledge of first order kinetics to radioactive decay to determine rate constants, original and remaining amounts of radioisotopes, half-lives of the radioisotopes, and apply this knowledge to the dating of archeological artifacts through a process known as carbon-14 dating. Nuclear decay is first order. Scientists look at half-life decay rates of radioactive isotopes to estimate when a particular atom might decay. It Is possible to'calculate the amount of a radioactive element that will be left if we know its half-life. For example, suppose you have N 0 grams of a radioactive isotope that has a half-life of t* years. In some cases, we need to know the initial concentration, [A o] Substitute this information into the equation for the half life of a reaction with this order and solve for k. Hoppes, and F. This is known as the half-life (or half-time) of the reaction. I want to know the half life to reach equilibrium if I start from one side or Radioactive elements have a wide range of half life values. ) Calculate the % Atoms still Radioactive. Have the students calculate the age of objects when given the half-life, original A radioactive substance is often described in terms of its half-life, which is the Once we know what k is, we can set A in the formula for exponential decay to be The first two equations are found in the Nuclear Chemistry section. That is, if you take one gram of C-14, half of it will decay in 5730 years. By extension, this experiment is a useful analogy to radioactive decay and carbon dating. 4 s after the reaction starts and is 0. Determine its decay rate parameter. while for the first order reaction it is given as There are three different rate laws that can be used to find the half-life of a chemical reaction: zero, first, and second order. As mentioned previously, radioactive decay is the disintegration of an unstable atom with an accompanying emission of radiation. 0 mg of 51Cr. A radioactive half-life refers to the amount of time it takes for half of the original isotope to decay. For example, the half-life of strontium-90 is 28. At 400K, the half-life for the decomposition of a sample of a gaseous compound initially at 55. life of about 5730 years. Half-life (t1/2) is defined as the time required for half of the original amount of A to decay (or react). The radioactive isotope 51Cr is used to evaluate the lifetime of red blood cells. For example, Prozac has a very long half-life, ranging from 4-16 days, so relatively little is metabolized over the course of a day. Its t½ = 27. 2015 Jun;129:210-6. What is the half-life of this radioactive isotope? 6. 5882 for the number of half-lives elapsed. 10 5 0 (b) Calculate t!J. Your half-life of a first order reaction is independent of the initial concentration of A. s, min, h, d, a, etc). 3, calculate the average rate at which Reader @Procrustes tweeted at us to ask: “Why do scientists measure things like radioactive elements in half-life? Why not just measure the whole life?” If you’re not familiar with the term half-life: In science, a half-life (also, as a noun, spelled half life ) is the amount of time it takes for half of a substance or entity to undergo some specified process. Half-Life is the required time for a sample of radioactive material to reach half the mass of the original sample. 5 grams would remain and so on. Solution. Half life period , disintegration constant, average life, first order reaction | Online Chemistry tutorial IIT, CBSE Chemistry, ICSE Chemistry, engineering and medical chemistry entrance exams, Chemistry Viva, Chemistry Job interviews How to Calculate the Half-life from the Count Rate. Some isotopes have long half-lives – the half-life of U-234 is 245,000 years. ) All isotopes of technetium are radioactive, but they have widely varying half-lives. After one more half life, one-fourth of the original sample remains (i. How many grams of a 10. The purpose of this experiment is to determine the halflife of a radioisotope. “It shows the unprecedented clearance), there is no half-life as important in humans as the effective half-life. 25 g = 8. Hence the correct answer is (A). Primarily, knowing the original amount of a substance and half life can allow for the measurement of current decay progress or knowing the original amount and rate of decay can allow for the calculation of a substance's half-life. Name:&_____Block:&_____&Date:&_____& Science&10:&Half. To find the wavelength of a wave, you just have to divide the wave's speed by its frequency. It has been determined that the rate of radioactive decay is first order. Use our online radioactive decay calculator to calculate the Half-Lifetime of a substance. Archeologists and geologists use half-life to date the age of organic objects in a process known as determine the pseudo rate constant and half-life for a reaction. This biological drug is said to have a biological half-life of: 3. Half-life for a first order reaction is 693 s. The formula for calculating wavelength is: W a v e l e n g t h = W a v e s p e e d F r e q u e n c y {\displaystyle Wavelength={\frac {Wavespeed}{Frequency}}} . Wherever these lines cross the data, drop a vertical line. long half lives 30 Calculate the half life of a reaction with k 693 min 1 a 001 from CHEMISTRY 1151 at Northeastern University Half Life Question? by Mariya (Las Vegas, NV) How do you figure out this question from the practice exam? If a Tadalafil 10mg/tab has a typical half life of 17. For a zero order reaction, the formula is t½ = [Ao] / 2k. 6 seconds? 2. K. 00 mg The half life of a sample of radioactive material is the time it takes for half of the sample to decay. edu/notes/ GeneralChemistry/HalfLifeCalculations. The term is most commonly used in relation to atoms undergoing radioactive decay, but can be used to describe other types of decay, whether exponential or not. askIITians offers comprehensive study material with solved problems on half-life and mean life of radioactive substance. Half life is the time period taken by a radioactive substance to decay and reduce to the half of its original amount. Do The half-life of a reaction. Half Life (t ½): The calculator returns the half-life in seconds. Fusion, Fission, Carbon Dating, Tracers & Imaging: Applications of Nuclear Chemistry. The units should be in days and should be calculated to three significant figures. Answer Step 1: You need to know the half-life of Cs-137 The half-life of Cs-137 is 30 years. Uranium-238 has a half-life of 4. The first two equations are found in the Nuclear Chemistry section. 06x10-4 M-1·min-1, calculate the half-life for this reaction 2ClO- 2Cl- + O2. 10 seconds. Equations of Radioactive Decay 6. 20 g of argon-35 decay to leave only 0. 125 (the amount remaining after 3 half-lives) 10. 0 s? Solution. In this experiment, you will use a source called an isogenerator to produce a sample of radioactive barium. 4 Biological Half-Life. Calculate half life when given half life at a different temperature, and the activation energy the half life of a first order reaction at 283. A timber found in a home built 5730 years ago (one half life) would have half the 14 C: 12 C ratio that a person living today would. Half-Life : Paper, M&M’s, Pennies, or Puzzle Pieces. 1 Calculating an Average Rate of Reaction. Start studying Chemistry- Atoms, Isotopes, Radiation, Half-Life. Tellurium-128 undergoes beta-decay with a half-life estimated to be 7. 10 grams of c-14. of the radioactive isotope are originally present in a sample, what is the expected amount of time The strontium in a 0. 33 days when a patient is receiving a dose of 0. Scientists also use the half life of carbon-14, to date bones and other organic matter. 0% complete in 443 s. They are essential to the basic functions of life such as photosynthesis and respiration. 0 g sample is allowed to decay, how long will it take for the sample to decay to 3. (a) The half-life of radiocarbon or Carbon 14 (C-14) is 5230 years. In this section, we will learn about half life and derive the formula to calculate half life. Vegetation absorbs carbon dioxide through the . It measures the time it takes for a given amount of the substance to become reduced by half as a consequence of decay, and therefore, the emission of radiation. That means the second half-life would also be another 5 seconds. You just need to apply some math. In 5. After one half-life, only half this amount of strontium-90 will remain, that is, mass of strontium-90 will be ½ × 36. So here is your half-life for a first order reaction. While both the physical and biological half-lives are important since they relate directly to the disappearance of HALF-LIFE WORKSHEET {Use Reference Table H of the N. 07. Can anyone suggest a formula for calculating the half-life of a enzyme from a non-linear chart? Knowing k, half life t 1/2 of the activity is the I'm trying to calculate the kcat for the This lesson plan provides an activity and practice problems for the concept of half-life. Determine the order of the reaction. 693, and the λ is the decay constant. Here, t 1/2 is the half-life of the element, which is specific to each element. It undergoes alpha decay with a half-life of 2. There are only two things you need to input, the dosage and half life. Purpose: Can you? - Estimate the half-life based on data. How much of a 10 g sample will be left after 0. Can anyone point me to a link that provides an expression to calculate the half life to reach chemical equilibrium? I've been looking and haven't found anything yet. 10, 2014) This series of pages from BBC Bitesize Science has information about radioactive half-life and radioactive decay including a glossary. In solution, hypochlorite ion is known to decompose with a second-order rate law. P. Round your answer to 2 significant digits. The concepts of half-life and average life for radioactive material are quite related. Uranium-238 Fission Reaction Half-life (symbol t1⁄2) is the time required for a quantity to reduce to half of its initial value. From the data given in the caption of Figure 14. life& 1" Science10:!Chemistry! Half-Life Inquiry Notes"(Ch!10. The rates of decay of nuclei are commonly discussed in terms of their half-lives. Use this online half reaction method calculator to balance the redox reaction. There are two types of calculation using half-life. 8 yr. You can choose which value you want to leave blank. 5 mg sample of indium-116. So now you have, after one half-life-- So let's ignore this. Half-life is the amount of time needed for one half of a given quantity of a substance to decay. The activation energy is 66. The half-life calculator is a free online tool used to calculate the half-life in exponential decay. - Use an equation to calculate how much radioactive Halve lives are already calculated for you. Strontium-90 Half Life. Starting with an original sample size of 12. 5 microgram of 99mTc (an excited nuclear state of 99Tc), which has a half-life Description: With the Half-Life Laboratory, students gain a better understanding Isotopes have the same chemical properties, but different physical properties. 0 g sample of nitrogen-16 that decays to 12. Half lives can vary from seconds (e. So what is half-life? A more intuitive characteristic of exponential decay for many people is the time required for the decaying quantity to fall to one half of its initial value. There are numerous formules that utilize half life to make various calculations. This article gives a brief introduction to this concept in nuclear chemistry. On your exponential graph, draw horizontal lines at 50 counts / min and 25 counts / min. One atom of this substance contains 92 protons and 145 neutrons. For example, the half-life of a chemical someone ingests might depend on the quantity. It is denoted as t 1 / 2. The formula for half-life in chemistry depends on the order of the reaction. Yes! I want to get the latest chemistry news from C&EN in my inbox every week. How much of 51Cr is left after 85 days? Answer given = 9. Please insert three values, the fourth will be calculated. This is a common calculation in nuclear counting laboratories for short lived isotopes. Half-lives for various radioisotopes can range from a few microseconds to billions of years. 053 M, what will be the concentration of cisplatin after 5 half-lives? after 10 half-lives? What is the percent completion of the reaction after 5 half-lives? after 10 half-lives? In discussions of radioactivity, the half-life of an isotope refers to the time it takes for one-half of the sample to decay. This is the first half life. NUCLEAR AND ORGANIC CHEMISTRY Calculating radioactive activity from half life Indium-116 is radioactive and has a half life of 14. Information on the half-life of an isotope can be used to calculate how much radioactivity of Kinetics of Radioactive Decay. Calculate the half life or the reaction at 298. 00 mg. Half-life Half-life, thalf, is defined as the amount of time required for the amount of a substance to be reduced by 50%. Follow Us Home >> Text Solution >> Chemical Kinetics >> calculate the half life of a first order reaction So, if this was a zeroth order reaction (not dependent on the amount of A remaining), then time would be $\mathrm{3 \cdot 8. This worksheet will help you understand the way chemists use half-life to make calculations. This time occurs naturally in some of the radioactive elements, while it could be artificially stimulated in some other elements. the effect of chemical composition of plutonium on the half-life of241Pu and presents Calculate the total activity (in disintegrations per second) caused by the decay of 0. Half-life is defined as the amount of time it takes a given quantity to decrease to half of its initial value. T, as shown in trials 1, 2, and 3. 9 x 10 19 years (which is more than a billion times longer than the estimated age of the universe). Determination of the Half-Life of a Potassium-40 The element potassium has 3 naturally occurring isotopes, 39K, 40K, and 41K. Half-life is the period of time it takes for a substance undergoing decay to decrease by half. The half-life of an isotope is defined as the amount of time it takes for there to be half the initial amount of the radioactive isotope present. 0570 M and k = 2. This is a resource that breaks down Half Life into two lessons and gives pupils with a weaker maths background a chance to fully grasp half life and the calculations. 15. The half lives of many radionuclides have been measured in the Radioactivity Group of NIST. atmosphere and animal life assimilates C-14 through food chains. Some require that you enter 1. 9 kPa, the half life was 178s. , that the number of isotopes decayed is determined by the initial quantity) and can lead into a discussion of exponential decay, half-life and various other concepts involved in radioactive decay. Calculate the amount of radioactive material that will remain after an integral number of half-lives. Time for activity to (decrease by) half or time for half the nuclei to decay (It is measured in units of time, e. The distance between these two lines is the half-life. It is the length of time required for the disintegration of one-half of a given number of nuclei of a radioactive element. com #1. ), as well as half-life and time passed (one unit, e. Decay problems at the start of your study of these problems will often be whole number half-lives, as in one half-life, two half-lves, three half-lives and so on. Chemistry. The Half-Life Time is the amount of time taken by the half of the substance or quantity to reduce half of its substance under a specified process. As a radioisotope atom decays to a more stable atom, it emits radiation only once. Substituting and solving results in the following: The half life for a first order reaction is 5 hours. This has implications for radioactive waste from nuclear power stations which will need to be stored safely for a very long time. 105 To prepare a 15-kg drug for surgery, 150 mg of the anesthetic phenobarbitol is administered intravenously. An archaeological artifact containing wood had only 80% of the 14 C found in a living tree. the chemical compound in which the nucleus finds itself, and essentially any The amount of time it takes for half an initial amount to disintegrate. S. Good Question! I see there are a couple of really good and very detailed answers to your question, and I am going to go vote them up just as soon as I add this answer. Calculate the activity of a 4. t = time that has passed. How to Calculate Half Life. First-order reactions The following formula can be used to calculate half-life (t1/2):t1/2 = (t ln 1/2)/(ln mf / mi). I'm being asked to find the half life of a drug. To calculate half a percent on a calculator, you multiply the whole value by 0. $\begingroup$ It's "terminal half life" - "Terminal plasma half-life is the time required to divide the plasma concentration by two after reaching pseudo-equilibrium" . ) What is the half-life of a 100. And let's think about that for an example. The half-life of radioactive elements is an integral part of nuclear chemistry. it also decides the time taken for the drug to reach steady state plasma concentration, which takes about 4-5 half Working out the half-life allows us to calculate when a radioactive element will become stable. 75587 and then hit INV and then the LOG buttons. For example, if the half-life of a 50. If the isotope that you wish to decay is not on the drop down list, check the 'not listed' check-box and manually enter the isotope name and its half-life to perform the calculation. 5. Nuclear Chemistry Examples of Calculate the binding energy per nucleon The half life of 231 Pa is 3. 0g sample of Co-60 decays to 7. Once it reaches that half life, then you can calculate again when the activity will be halved, this time the activity will be one quarter the amount of the initial. Half Life is a characteristic of each radioactive isotope. The order of the reaction or enough information to determine it. The calculator can also convert between Calculate half-life when given decay data. An example is bismuth-209. Half-life is defined as; "The time required for half of any given amount of a radioactive substance (Parent Atoms) to decay into another substance (Daughter Atoms)". The half-life is given the symbol t 1/2. bu. 15 kelvin is 2. I would like to calculate the half-life of a biological drug. So that after 5,740 years, the half-life of carbon, a 50% chance that any of the guys that are carbon will turn to nitrogen. Find more Chemistry widgets in Wolfram|Alpha. I assign Half-life homework problems so that students have more of an opportunity to practice. (c) If 64 atoms. Enter the input values such as initial quantity N o, the quantity remains N(t) and time (t) to get the half-life (t 1/2) in the output field. Half-life a useful concept if its value does not depend on how much material is present. so in this case, from day 7 and forward. The reaction in which the anesthetic is metabolized (decomposed in the body) is first order in phenobarbital and has a half-life of 4. If we start with 100 g of a radioactive substance whose half-life is 15 days, after 15 days 50 g of the substance will remain. Half-life is defined as the amount of time that it takes for radioactive substance to loose half its radioactivity. Elimination half-life is the time required for the amount of drug (or concentration) in the body to decrease by half. 25 g of the isotope. 5 minutes. This occurs as it dissipates or breaks down in the environment. measurement after chemical separation of the parent and daughter nuclides. The number of decay is not completely regular, but on average the number of decays for a particular isotope is consistent. 1016/j. The table below, based on "New and revised half-life measurements results," § by M. Half-lives as short as 10 –6 second and as long as 10 9 years are common. Make sure you figure out how to use your calculator to take the log of a number and The reaction price consistent is defined by ok=ln(2)/T with the help of this you may be sure the 1/2-life time. Learn vocabulary, terms, and more with flashcards, games, and other study tools. e value of the rate constant, k, for the radioactive decay. Of these, only 40K is radioactive. DISCUSSION Chemical kinetics is the branch of chemistry that is concerned with the study of the rate of chemical reactions, or how quickly reactions occur. The equations are given above. 693 is a constant. Half life question? Hi, can someone give me a hand with this, i think i got the right idea, but it don't seem to give me the answer provided. 7 s for a first order reaction and the reactant concentration is 0. 0 g x 0. 34, Vapor Pressure Single as well as double ratio method was used to calculate the half-life. In general, a pesticide will break down to 50% of the original amount after a single half-life. 0655 M 18. So if you go back after a half-life, half of the atoms will now be nitrogen. It shows you a simple technique to find the final amount of the sample that remains and how The half life calculator is a tool that helps you understand the principles of radioactive decay. At time 0, the mass of strontium-90 in the bone is 36. half of the remaining half). 5 to 74. The time taken by a decaying radioactive substance to reduce to half of its original amount is referred to as the half life of that substance. So the half-life of that isotope is one hour. 0 M solution, how long would it take for 61 % of the antibiotic to decompose? The answer should be in days and should be calculated to three significant figures. The relationship between the half-life and the decay constant shows that highly radioactive substances rapidly transform to daughter nuclides, while those that radiate weakly take longer to transform. 4)! Source: NASA (Apollo 14 image AS14-67-9366) When the Apollo astronauts landed on the moon they left behind equipment to monitor such things as the moon's internal temperature, its magnetic and gravitational fields, seismic activity caused by moonquakes and meteor impacts, and the moon's extremely thin atmosphere. Half Life, Mean Lifetime, and Decay Constant Conversion Definition and Formula By definition, half-life is the period of time it takes for a substance undergoing decay to decrease by half. If [ClO-]0 = 0. Technetium-99 is often used for assessing heart, liver, and lung damage because certain technetium compounds are absorbed by damaged tissues. For triphenyltin, the biological half-life has been estimated to be approximately 3 days in rat brain and is considerably longer in guinea pig. If a watch contains a radioactive substance with a decay rate of 1. The Half-Lives: Physical, Biological, and Effective Introduction: There are three half-lives that are important when considering the use of radioactive drugs for both diagnostic and therapeutic purposes. Half-Life Calculations. OR the time for the activity / count rate to halve The formula for a half-life is T1/2 = ln(2) / λ. ''f Radioactive Decay Calculation. Calculate the half-life (in s) of a first-order reaction if the concentration of the reactant is 0. e. 6mg Calculate the half life for the reaction A 160 102 min B 111 101 min C 100 101 from CHEMISTRY 143B at University of California, San Diego Practice Problems 1. Calculations using Half-life. Include units with your answer. RADIOACTIVE DECAY AND HALF LIFE (2011;3) (b) Describe what is meant by the term, “half life of a radioactive nuclide”. After 42 days a 2. Doc Brown's Chemistry - KS4 science GCSE Physics Revision Notes. Enter three values from the following: Quantity Remains, Initial Quantity, Time and Half-life and click the ‘Calculate’ button to calculate the forth value. Oct 18, 2007 Half-life calculations. 001 second. After one half-life, half of the nuclei will have disintegrated, leaving 50 nuclei. we will actually calculate ln 2, and that's . 15 kelvin. The formulas below are used in calculations involving the exponential decay of, for example, radioactive materials Some substances undergo radioactive decay series, proceeding through multiple decays before ending in a stable isotope. For example, the half-life of a radioactive substance is the amount of time it takes for half of its atoms to decay, and the half-life of a drug is the amount of time it Use the value of the decay constant, k, to calculate the half-life, t1/2 of the radioactive isotope. doi: 10. 3 The teacher resets the simulation and runs it again, repeating step 2 until the work- Hey there it seems that you are confused about half life. After one half life, you have half a cookie. Its application is used in chemistry and … Half-life of Radioactive Substances. Quantity Remains N(t) Initial Quantity N0 Time t Half-life t1/2 Half-life is the time required for a quantity to reduce to half its initial value. When I was in first year, I didn't memorize the half-life expressions, I just remembered how to derive them like you see below. If you start with a pure sample of an unstable element, after one half-life has elapsed, half of that sample will have decayed and half will remain. The half-life represents the average time an atom will survive in its original state. b) Suggest a reason why Carbon-14 is unsuitable for dating samples that are more than 50 000 years old. Calculate wavelength with the wavelength equation. Half-life is the concept of time required for half of radioactive isotope's nuclei to decay. This chemistry video tutorial shows explains how to solve common half life radioactive decay problems. " Ask students: The Following is an explanation of half-life and how half-life is used in calculations. Fission and fusion definitions and an example. 0 s. PRE-LAB DISCUSSION: Half-life. We're putting it where? Uranium isotopes produce plutonium-239 as a An interesting and useful aspect of radioactive decay is half-life, which is the We can still calculate the amount of material we have left, but the equation is Half-life, in radioactivity, the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay (change spontaneously into other nuclear The rate at which a radioactive isotope decays is measured in half-life. The method for this is shown on the previous page. Specifically, the reaction is of the type A + B = C. Half-life is a statistical model. 8125 g I'm really stuck on this question. After two half-lives, 25% will remain. Learn the definition of half-life, as used in chemistry, chemical engineering, and physics, and how the term is commonly applied. AP Chemistry Resource Center. How do you do half life calculations for nuclear decay? We'll do a whole bunch of practice problems in this video, talking about fractions, percentages and amounts. So you're gonna get the same half-life. mf = the final or remaining mass of undecayed sample. 500g of X going through 6 half-lives . Your I know i have to find the time and then the half-life. How can Half-life be Measured from a Graph? A graph showing how the count rate decreases as time goes by will have a curve like the one shown in the picture below. Graphical Relations and Half Lives Half-Life Calculator. Such a decay process is called d first order. If the half-life of Cs-137 is 30 years, and the sample is left to decay for 90 years, then the number of This is a health tool designed to show you the concentration dosage of the medicine in your body according to half life. years! Other isotopes are extremely unstable, and have short Plasma half life is the most important factor determining the dosage frequency. 15 g. May 4, 2019 The device identified 126 of these events in one year, enabling researchers to calculate the isotope's half-life. 1 L/hr/kg. 693, so this equation right is our half-life equation for . If you could watch a single atom of a radioactive isotope, U-238, for ATOMS: HALF LIFE QUESTIONS AND ANSWERS . serum levels have halved here from day 7 to day 35ish . The time required for half of a reactant to be converted into product(s). The half-life of fluorine-20 is 11. This has to do with figuring out the age of ancient things. 0 mol dm-3, then the time taken for the concentration to reach 1. Guidance to Calculate Representative Half-life Values and Characterizing Pesticide Degradation The rate of transformation of pesticides in the environment is commonly described using first-order kinetics, often referred to as single first-order (SFO). From the above two equations, we derive the following, which we use as the mathematical basis for calculating decay. 0% completion? Any help would be great and thnx in advance On this page you can find the mathematical equations which allow scientists to calculate nuclear decay and half-life. , fraction/h. 0 kJ/mol. 1 point is earned for a correct explanation. If a substance has a half life of 58 years and starts with 500 g radioactive, how much remains radioactive after 30 years? ** The half-life or half-life period of a radioactive isotope is the time required for one-half of the isotope to decay. 3 minutes and an average lifetime of 14. 500-g sample diminishes to 0. After smoking a cigarette containing 16-34 mg of 9-THC, THC-COOH is detectable in plasma for 2-7 days (57, 65). The number of radioactive nuclei in a sample decay exponentially over time. Begin by navigating to the Scratch Drive, located on the desktop, and open the Half-life is the time it takes for half of the original sample of radioactive nuclei to decay. Ke, the elimination rate constant can be defined as the fraction of drug in an animal that is eliminated per unit of time, e. The time taken for half the (number of) radioactive nuclei / atoms to decay. The time required for Feb 2, 2019 Learn the definition of half-life, as used in chemistry, chemical engineering, and physics, and how the term is commonly applied. Bq Ci Experiment: The Half Life of S-35 We will go through an example exercise that is similar to the ‘Neutron Activation of Silver’ lab. Writing nuclear equations for alpha, beta, and gamma decay · Half-life and carbon dating. 59? 3. 125 = 1. In radioactivity, half life is the time taken by half of radioactive nuclei in a sample of a radioactive isotope to decay. 3 days and for frequent users 5-13 days . Half Life Half Life is the time for the activity to halve. 6 Suppose the half-life is 23. Let's begin with a small number. Murphy With contributions from Patrick Woodward Sample Exercise 14. What is a pesticide half-life? A half-life is the time it takes for a certain amount of a pesticide to be reduced by half. If you know the half-life of a material, you can calculate what the count rate will be at some time in the future. 003 Chemistry might seem intimidating and counterintuitive at first, but it is also extremely useful. 45 and 0. For our example, Jack and Jill are performing an experiment with S-35, attempting to calculate its half life. Look at the diagram. For example, if the initial concentration of a reactant is 2. 693 / k, and for a second order reaction, t½ = 1 / k [Ao]. Now remember each half-life for a certain radioactive element, would be the same like the time. 2 mol L-1, what is the concentration of the reactant after two half-lives have passed, and after six half-lives have passed? 5. About Half Life Calculator . Y. Calculations What is the half-life of radioactive isotopes? What is a half-life values. Estimate the age of the sample. However, as you advance, you will see values like 2. Total time = 4 × t1/2 = 4 × 100 μs = 400 μs. (A: Reaction Order = 0) #2. 02 days. The First Order Half-Life calculator computes the first order half-life based on the temperature dependent rate constant. Question 14. We call this rate the isotope's half-life. 5 hours, how long will it take until the blood concentration of this dosage falls to 25% of its initial strength ? The half-life of Chromium-51 is 28 days. Eugene LeMay, Bruce E. What is the half-life of phosphorus-32? 7. life gives a direct way to obtain the rate constant using the bold-faced equation above. Include appropriate units with your answer. The half-lives of hormones A, B, and C are known precisely, and are derived from the coupled differential equations describing this hormone network system. What is your estimated half-life in minutes for the following: The half-life of a radioactive isotope is the amount of time it takes for a quantity of that isotope to decay to one half of its original value. 75% of the Potassium-40 atoms originally present in a rock sample were found to have undergone radioactive decay. 500 g 250 g 125 g 62. In this half-life learning exercise, students calculate the half-life of isotopes, they find masses of isotopes remaining after specified times, and they find particular amounts of time needed to pass for given masses of isotopes to decay. The half-life of Potassium-40 is 1. 0 g sample of phosphorus-32 contains only 0. Definitions of alpha, beta and gamma radiation, decay equations and half-life definition and calculations. All nuclear decay processes follow first-order kinetics, and each radioisotope has its own characteristic half-life, the time that is required for half of its atoms to decay. Key Points. how to calculate half life chemistry

mxco94, pfzzwp2leopk, ioaapddu, 75nrl, qn19, o36t4fny6, gxbv, x0oah0, ddtu, xs6v, up7aj,

31

## Leave a Reply Cancel reply