Question

The radium and uranium atoms in a sample of uranium mineral are in the ratio of $1: 2.8 \times 10^{6}$ If half-life period of radium is $1620$ year, the half-life period of uranium will be:

• A. $4.53 \times 10^{9}$ year
• B. $45.3 \times 10^{9}$ year
• C. $4.53 \times 10^{10}$ year
• D. $45.3 \times 10^{10}$ year

Answer 1

Answer: (A)

$4.53 \times 10^{9}$ year

Answer 2

$\frac{N_{A}}{N_{B}}=\frac{\left[t_{1 / 2}\right]_{A}}{\left[t_{1 / 2}\right]_{B}}$ or $\frac{1}{2.8 \times 10^{6}}=\frac{1620}{\left[t_{1 / 2}\right]_{B}}$ or $\left[t_{1 / 2}\right]_{B}=1620 \times 2.8 \times 10^{6}$ $=4.536 \times 10^{9}$ year