The half life of a radioactive material is 5 years. The probability of disintegration for a nucleus in 10 years is?
The half life of a radioactive material is 5 years. The probability of disintegration for a nucleus in 10 years is?
The correct option is B 0.25
Consider an isotope whose half-life is HL years, and you wish to calculate the probability that any particular atom of that isotope will decay within T years.
After some thought, and considerable doodling with pencil and paper, you realize that the probability that, for a half-life of 5 years ( HL = 5 ), that atom has a fifty % chance of decaying within five years ( T = 5 ). Half of the sample will have decayed before the five years is up. The probability of decay ( P ) within five years is 0.50.
With extraordinary insight, you intuit that the probability P, given HL and T is
P = HL2XT ; this is simply a mathematical expression of the fact of the probability described above P=22×5=0.5You already know that after two half-lives ( 10 years ), only a quarter of the sample will remain: so you are delighted to plug in the number 10 for the ten years ( T = 10 ) you want the probability of decay for - if you follow - is as follows:
P ( 10 years ) = 52×10 = 0.25 - the same answer you already know from the knowledge that after two half-lives, only 0.25 of the original sample remains undecayed.
Please notice that this is an empirical equation ( From the word “intuit”, above ). When you take Physical Chemistry ( where you learn about rates of reaction ) and Nuclear Chemistry ( where the mathematical and nuclear subtleties of radioactive decay are studied ) there is a truly ab initio derivation of
P =HL2XT.
Consider an isotope whose half-life is HL years, and you wish to calculate the probability that any particular atom of that isotope will decay within T years.
After some thought, and considerable doodling with pencil and paper, you realize that the probability that, for a half-life of 5 years ( HL = 5 ), that atom has a fifty % chance of decaying within five years ( T = 5 ). Half of the sample will have decayed before the five years is up. The probability of decay ( P ) within five years is 0.50.
With extraordinary insight, you intuit that the probability P, given HL and T is
P = HL2XT ; this is simply a mathematical expression of the fact of the probability described above P=22×5=0.5You already know that after two half-lives ( 10 years ), only a quarter of the sample will remain: so you are delighted to plug in the number 10 for the ten years ( T = 10 ) you want the probability of decay for - if you follow - is as follows:
P ( 10 years ) = 52×10 = 0.25 - the same answer you already know from the knowledge that after two half-lives, only 0.25 of the original sample remains undecayed.
Please notice that this is an empirical equation ( From the word “intuit”, above ). When you take Physical Chemistry ( where you learn about rates of reaction ) and Nuclear Chemistry ( where the mathematical and nuclear subtleties of radioactive decay are studied ) there is a truly ab initio derivation of
P =HL2XT.
