Question

The half-life of a radioactive substance against $\alpha -$ decay is $1.2\times {10}^{7}s$. What is the decay rate of $4.0\times {10}^{15}$ atoms of the substance?

• A. $4.6\times {10}^{12}$ atoms/s
• B. $2.3\times {10}^{11}$ atoms/s
• C. $4.6\times {10}^{10}$ atoms/s
• D. $2.3\times {10}^8$ atoms/s

Answer 1

The correct option is D $2.3\times {10}^8$ atoms/s

The half life of a radioactive substance against $\alpha -$ decay is $1.2\times {10}^{7}s$.
The decay constant $\lambda =\frac{0.693}{T}=\frac{0.693}{1.2\times {10}^7}$
The expression for the decay is $\frac{dN}{dt}=\lambda N$
The decay rate for $4.0\times {10}^{15}$ atoms of the substance $\frac{dN}{dt}=\frac{0.693}{1.2\times {10}^7}\times 4\times {10}^{15}=2.3\times {10}^{8}atom/s$