Question

A radioactive element has half-life period of $600$ yr. After $3000$ yr, what amount will remain?

• A. $\frac{1}{2}$
• B. $\frac{1}{16}$
• C. $\frac{1}{8}$
• D. $\frac{1}{32}$

Answer 1

Answer: (D)

$\frac{1}{32}$

Answer 2

We know that $n=\frac{t}{T}$ Given, $t=3000\text{ }yr,\text{ }T=6000\text{ }yr$ $n=\frac{3000}{600}=5$ Then, $\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{n}}$ $\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{5}}=\frac{1}{32}$