Question

A radioactive sample has a half-life of $10$ minutes. If $64$ nuclei are contained in the sample the number of nuclei that would decay after $50$ minutes is:

• A. $2$
• B. $5$
• C. $59$
• D. $62$

Answer 1

Answer: (D)

$62$

Given: Half life, $t_{1/2}=10min$

We know that: $t=n{t}_{1/2}$

$\Rightarrow n=\frac{t}{t_{1/2}}=\frac{50}{10}=5$

$\Rightarrow N=\frac{N_0}{2^n}=\frac{64}{2^5}=2$

$\therefore$ Number of nuclei decayed during $50$ minutes $=N_0-N=62$