Question

1 mg gold undergoes decay with 2.7 days half-life period, amount left after 8.1 days is.

• A. 0.91 mg
• B. 0.25 mg
• C. 0.5 mg
• D. 0.125 mg

Answer 1

Answer: (D)

0.125 mg

Answer 2

$N = N_{0}\left( \frac{1}{2} \right)^{n} \Rightarrow N = N_{0}\left( \frac{1}{2} \right)^{t/T_{1/2}}$

$\Rightarrow N = 1 \times \left( \frac{1}{2} \right)^{\frac{8.1}{2.7}} = \left( \frac{1}{2} \right)^{3} = \frac{1}{8} \Rightarrow N = \frac{1}{8}mg = 0.125\mspace{6mu} mg$