A substance has a half life of 5 years. For a nucleus in a sample of the element, what is the probability of decay in 10 years? Answer 3 Follow Request More Ad by Amazon Pay.   Amazon Pay. Get 25% cashback up to ₹50 on bill payments with Amazon Pay UPI. #BadaHogaRupaiyaa. Learn More 2 ANSWERS Jerome Zoeller, Ph.D from The University of Texas at Austin (1987) Answered Jun 30, 2018 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 = HL / ( 2 X T ) ; this is simply a mathematical expression of the fact of the probability described above P = 5 / ( 2 X 5 ) = 0.5 You 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 ) = 5 / ( 2 X 10 ) = 0.25 - the same answer you already know from the knowledge that after two half lives, only 0.25 of the original sample remaims undecayed. Please notice that this is an emperical 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 = HL / ( 2 X T ) .