Question

The half-life of thorium X is 3.64 days. After how many days will 0.1 of the mass of a sample of the substance remain undecayed?

• A. 12.1 days
• B. 24 days
• C. 60 days
• D. 4 days
• E. 14 days

Answer 1

Answer: (A)

The decay constant is
$\lambda =\frac{0.693}{T}=\frac{0.693}{3.64}=0.1904/day$
Also, $N=N_0{e}^{-\lambda t}$
Given, $\frac{N}{N_0}=0.1=10^{-1}$
$\therefore 10^{-1}=e^{-\lambda t}$
$\Rightarrow e^{\lambda t}=10$
$\lambda t=lo{g}_{e}10$
$=2.3026\times lo{g}_{10}10$
$=2.3026\times 1$
$\therefore t=\frac{2.3026\times 1}{\lambda }=\frac{2.3026\times 1}{0.1904}=12.1days$