Question

it takes 60 days for 1024 grams of element XY to decay to 32 grams. what is the half life of element XY

Answer 1

Answer:

The half life of element XY is 12 days

Explanation:

Given:

Time taken for  1024 grams to decay into 32 grams  = 60 days

To Find:

The half life of element XY = ?

Solution:

The Half life is calculated by

$N = N_0 (\frac{1}{2})^{\frac{t}{t_{\frac{1}{2}}}$

$t_{\frac{1}{2}}$ =$\frac{t}{log_{\frac{1}{2}}( \frac{N(t)}{N_0})}}$

Substituting the values,

$t_{\frac{1}{2}}$ =$\frac{60}{log_{\frac{1}{2}}( \frac{32}{1024})}}$

$t_{\frac{1}{2}}$ =$\frac{60}{log_{\frac{1}{2}}(0.03125)}}$

$t_{\frac{1}{2}}$ =$\frac{60}{5}$

$t_{\frac{1}{2}}$ = 12