Question

A sample of radioactive substance has $8\times {10}^8$ nuclei. Its half life is 20 minutes. The number of nuclei that will decay in one hour is

• A. $2\times {10}^8$
• B. $4\times {10}^8$
• C. $1\times {10}^8$
• D. $7\times {10}^8$

Answer 1

Answer: (D)

: For radioactive decay, $\frac{N}{N_0}={\left(\frac{1}{2}\right)}^{t/T}$ where $T=$ half life $N=N_0{\left(\frac{1}{2}\right)}^{t/T}=(8\times {10}^8)\times {\left(\frac{1}{2}\right)}^{60/20}=\frac{8\times {10}^8\times 1}{8}$ $=1\times {10}^{8}nuclei$ . $\therefore$ Number of nuclei left undecayed $=1\times {10}^8$ $\therefore$ Number of nuclei that have decayed $=(8-1)\times {10}^8=7\times {10}^8$ .