= N 0 (1/32) = N 0 / 32 N = N 0 / 32 Amount left after 5 half lives is 1/32 of initial amount. Question 9 ) How much of a radioactive element is left after 5 half lives ? Solution ) How much of 1H3 should be taken initially so that it remains 4 Kg after 26.6 years ? Solution ) Question 8) Half life of 1H 3 is 13.3 years.
Calculate the disintegration constant ? Solution )Īmount of Thorium left ‘N’ = 100 – 87.5 = 12.5 gm Question 7) Thorium is 87.5 % disintegrated in 48 days. K =0.693 /t 1/2 = 0.693 / 30 K = 0.0231 days -1 Question 6) Starting with 16 atoms of a radioactive element, how many atoms are left after 4 half lives? Solution ) Calculate the disintegration constant of the element ? Solution ) Question 5) The activity of a radioactive element remains 12.5% in 90 days. N= 10 (1/2) 2 N =2.5 grams Question 4) Half life of 83 I 125 is 60 days.How much its radioactivity remains after 180 days ? Solution ) How much of thorium remains in 48 days ? Ans – = 2×2.5×10 5 T=5×10 5 years Ans Question 3) 10 gram thorium remains 5 grams in 24 days. In how many years it will remain 25% of original amount? Ans. Question 2) Half life period of U 234 is 2.5×10 5 years. Calculate its disintegration constant & average life? Ans.Īverage life = 1.44 × t 1/2=1.44×10 Average life = 14.4 years Ans. For radon 217, the chance of decay is large: Its half-life is one thousandth of a second.Source : Question 1 ) Half life period of a radioactive element is 10 years. For uranium 238, the chance of decay is small: Its half-life is 4.5 billion years. The cubes, for instance, have a longer half-life than the pennies. The smaller the chance of decay, the longer the half-life (time for half of the sample to decay) of the particular radioactive isotope. The chance that a particular radioactive nucleus in a sample of identical nuclei will decay in each second is the same for each second that passes, just as the chance that a penny would come up tails was the same for each toss (1/2) or the chance that a cube would come up red was the same for each toss (1/6). In this model, the removal of a penny or a cube corresponds to the decay of a radioactive nucleus. However, if you repeat the first toss many, many times, the average number of coins that decay will approach 1/2 (or cubes that decay will approach 1/6). Rarely will exactly 1/2 of the coins or 1/6 of the cubes decay on the first toss. Tossing the coins or cubes is an unpredictable, random process.
After one toss, 5/6 remain after two tosses, 5/6 of 5/6, or 25/36, remain and after three tosses, (5/6) 3 = 125/216 of the cubes are left. (Each cube has six sides, and only one of those sides is painted red.) It takes three tosses for about half the cubes to be removed, so the half-life of the cubes is about three tosses. If you’re using painted wooden cubes, the probability that a cube will land red side up is 1/6. The half-life of the pennies in this model is about one toss. The time it takes for half of the remaining pennies to be removed is called the half-life. This type of pattern-in which a quantity repeatedly decreases by a fixed fraction (in this case, 1/2)-is known as exponential decay (click to enlarge photo below).Įach time you toss the remaining pennies, about half of them are removed. These numbers can be written in terms of powers, or exponents, of 1/2: (1/2) 1, (1/2) 2, (1/2) 3, and (1/2) 4. After the first toss, about 1/2 of the original pennies are left after the second, about 1/4 then 1/8, 1/16, and so on. Half-life, or t½, is the time that elapses before the concentration of a reactant is reduced to half its initial value. For a first order reaction, t½ 0.693 / k, and for a second order reaction, t½ 1 / k Ao.
For a zero order reaction, the formula is t½ Ao / 2k. Thus, about half the pennies are left after the first toss.Įven though half of the remaining pennies come up tails on the second toss, there are fewer pennies to start with. The formula for half-life in chemistry depends on the order of the reaction.
However, once a penny has come up tails, it is removed. The chance that any penny will come up tails on any toss is always the same, 50 percent.