Question

A sample initially contained 150 mg of radon-222. After 11.4 days only 18.75mg of the radon-222 in the sample remained. How many half lived have passed?

Answer 1

Answer:

A sample initially contained 150 mg of radon-222. After 11.4 days only 18.75mg of the radon-222 in the sample remained where 3 half-lives have passed

Explanation:

Given, the initial value of the sample, $A_0$ = 150mg

Final value of the sample or the quantity left, A = 18.75mg

Time = 11.4 days

The amount left after first half life will be ½.

The number of half-life is calculated by the formula

$\frac{A}{A_{0}}=\left(\frac{1}{2}\right)^{N}$

where N is the no. of half life

Substituting the values,

$\frac{18.75}{150}=\left(\frac{1}{2}\right)^{N}$

$\left(\frac{1}{2}\right)^{3}=\left(\frac{1}{2}\right)^{N}$

On equating, we get, N = 3

Therefore, 3 half-lives have passed.