Question

The half life of radium is $1600$ years. The fraction of radium atoms that remain undecayed after $4800$ years will be

• A. $\frac{1}{4}$
• B. $\frac{1}{16}$
• C. $\frac{1}{8}$
• D. $\frac{1}{32}$

Answer 1

The correct option is C $\frac{1}{8}$

Half life, $t_{1/2}=1600years$

Number of half lives in $4800years$ is $n=4800/1600=3$

So, fraction of radium atoms that remain undecayed is $1/2^n=1/2^3=1/8$