Question

4. The half-life of a sample has been defined as the time it takes for half of a sample to decay. The fifth-life can be defined as the time it takes for one-fifth of a sample to decay. Given these definitions, calculate the fifth-life of a sample that has a half-life of 29 years.

Answer 1

Half life = 29 years

Rate constant = 0.693/half life = 0.693/29 = 0.02389 year^-1

Let initial amount is (A0) 100.

Decayed amount = 100 * 1/5 = 20

Remaining amount (At) = 100 - 20 = 80

Using first order reaction;

K * t = 2.303 * log (A0/At)

0.02389 * t = 2.303 * log (100/80)

t = 9.34 years ....Answer