Question

Suppose a small quantity of radon gas, which has a half-life of 3.8 days, is accidentally released into the air in a laboratory. If the resulting radiation level is 20% above the safe level, how long should the laboratory remain vacated? (Hint: To start with, determine what fraction of the "resulting radiation level" is the maximum safe level.)

Answer 1

Answer:

1 day

Explanation:

Let the safe level = x

The current level = x + 0.2x = 1.2 x

Thus,

Half life = 3.8 days

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

Where, k is rate constant

So,  

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

$k=\frac {ln\ 2}{3.8}\ days^{-1}$

The rate constant, k = 0.1824 days⁻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

So,

$\frac {[A_t]}{[A_0]}$ = x / 1.2 x = 0.8333

t = ?

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

$0.8333=e^{-0.1824\times t}$

t ≅ 1 day

Lab must be vacated in 1 day.