Question

1.0 mg mass of radium have $3.68\times {10}^{18}$ atoms and its half-life is 1500 yr. How rnuch radium atom disintegrated of 1 mg radium in 3000 yr ?

Answer 1

According to the question

$1$mg of radium $\to 3.68\times {10}^{18}$ atoms

It has half life $1500$ years, then in $3000$ years

After one half life i.e., $1500$ years $\to \frac{3.68}{2}\times {10}^{18}$ atoms left

The, after another half life i.e., total of $3000$ years $\to \frac{3.68}{2\times 2}\times {10}^8$ atoms left

$\Rightarrow$ Atoms disintegrated $=3.68\times {10}^8-\frac{3.68}{4}\times {10}^8$

$=3.68\times \frac{3}{4}\times {10}^8$

$=2.76\times {10}^8$ atoms.