Question

Tritium has a half-life of 12.3 years. When the activity of a tritium sample has decreased to 6.25% of its original value, how many years have passed

Answer 1

Answer:

t = 49.20 years

Explanation:

Half life expression for first order kinetic is:

Half life = 12.3 years

$t_{1/2}=\frac{\ln2}{k}$

Where, k is rate constant

So,  

$k=\frac{\ln2}{t_{1/2}}$

$k=\frac{\ln2}{12.3}\ years^{-1}$

The rate constant, k = 0.05635 years⁻¹

Using integrated rate law for first order kinetics as:

$[A_t]=[A_0]e^{-kt}$

Where,  

$[A_t]$ is the concentration at time t

$[A_0]$ is the initial concentration

Given:

$[A_t]$ is 6.25 % of $[A_0]$. So,

$\frac {[A_t]}{[A_0]}$ = 0.0625

t = ?

$\frac {[A_t]}{[A_0]}=e^{-k\times t}$

$0.0625=e^{-0.05635\times t}$

t = 49.20 years