Question

The hall-life period of a radioactive substance is 140 days. After, how much time, 15 g will decay from a 16 g sample of the substance ?

• A. 140 days
• B. 280 days
• C. 420 days
• D. 560 days

Answer 1

Answer: (D)

560 days

From Rutherford - Soddy law, the number of radioactive nuclei left after n half - life's is
$N=N_o{\left(\frac{1}{2}\right)}^n$Given, $N=16-151g{N}_0=16$
$\frac{1}{16}={\left(\frac{1}{2}\right)}^n$
${\left(\frac{1}{2}\right)}^4={\left(\frac{1}{2}\right)}^n$
The time to decay 15 g of the substance is
$T_{1/2}\times n=140\times 4$
$=560$ days