Question

half-life of a radio isotope is 5 years. fraction of substance that decays in 15 years is:
option given:-
(a). 1/15
(b). 1/8
(c). 7/8
(d). 14/15

Answer 1

1--(5year)--> 0.5 --(5year)--> 0.25 --(5year)--> 0.125 = 1/8

Answer 2

Answer: (b). 1/8

Explanation:

To calculate the rate constant, we use the formula:

$\lambda =\frac{0.693}{t_{\frac{1}{2}}}=\frac{0.693}{5}=0.14 years^{-1}$

$N=N_o\times e^{-\lambda t}$

$\frac{N}{N_0}=e^-\lambda t$

Given t= 15 years

Putting values in above equation, we get:

$\frac{N}{N_0}=e^-0.14\times 15$

$\frac{N}{N_0}=0.125=\frac{1}{8}$