Question

5mg radioactive sample 90% disintegrate in 3 years then 99% disintegration will be in?
Ans. 6yrs

Answer 1

Explanation:

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Answer 2

Answer:

6 years

Explanation:

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:

90 % is decomposed which means that 0.9 of $[A_0]$ is decomposed. So,

$\frac {[A_t]}{[A_0]}$ = 1 - 0.9 = 0.1

t = 3 years

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

$0.1=e^{-k\times 3}$

k = 0.7675 years⁻¹

Also,  

Given:

99 % is decomposed which means that 0.99 of $[A_0]$ is decomposed. So,

$\frac {[A_t]}{[A_0]}$ = 1 - 0.99 = 0.01

t = ?

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

$0.01=e^{-0.7675\times t}$

t = 6 years