Question

A radioactive substance has $6.0$$\times {10}^{18}$ active nuclei initially. The time that should be required for the active nuclei of the same substance to become $1.0\times 10$${}^{18}$ is (if its half life is $40s$,log${}_{10}$$6=0.7781$ )

• A. $101.2s$
• B. $102.3s$
• C. $103.4s$
• D. $104.5s$

Answer 1

Answer: (C)

$103.4s$

$N_0=6\times {10}^{18}$
$t_{1/2}=40,N=1\times {10}^{18}$

$ln\frac{6}{1}=\left(\frac{.693}{40}\right)\times t$

$t=103.4s$