Question

Find the decay rate of the substance having $4\times {10}^{15}$ atoms. Half-life of a radioactive substance in $\alpha$ decay is $1.2\times {10}^7$

• A. $2.3\times {10}^8$ atom/s
• B. $3.2\times {10}^8$ atom/s
• C. $2.3\times {10}^{11}$ atom/s
• D. $3.2\times {10}^{11}$ atom/s

Answer 1

The correct option is A $2.3\times {10}^8$ atom/s

$N=4\times {10}^{15}atoms$

half life is $t_{1/2}=1.2\times {10}^{7}second$

so the decay constant will be $\lambda =\frac{0.693}{t_{1/2}}=0.5775\times {10}^{-7}/s$

Now the the decay rate can be calculated as $A=N\lambda =4\times {10}^{15}\times 0.5775\times {10}^{-7}atoms/s=2.31\times {10}^{8}atoms/s$