1 mg radium has `2.68xx10^18` atoms. Its half life is 1620 years. How many radium atoms will disintegrate from 1 mg of pure radium in 3240 years ?

Options

A. `2.01xx10^9`
B. `2.01xx10^18`
C. `1.01xx10^9`
D. `1.01xx10^18`

Answer

B

Explanation

`n=t/T_(1//2)=3240/1620`=2
As `N/N_0=m/m_0=(1/2)^n`
Mass of radium left after 2 half lives is `m=m_0(1/2)^n = 1xx(1/2)^2 =1/4` = 0.25 mg
Mass of radium disintegrated =1-0.25 =0.75 mg
Number of radium atoms disintegrated = 0.75 x 2.68 x `10^18=2.01xx10^18`