Question

The half-life of a radioactive substance is 40 years. How long will it take to reduce to one fourth of its original amount and what is the value of decay constant?

• A. 40 year, 0.9173/year
• B. 90 year, 9.017/year
• C. 80 year, 0.0173/year
• D. none of these

Answer 1

Answer: (C)

Here: $T_{1/2}=40$ years, $\frac{N}{N_0}=\frac{1}{4}$ From relation $\frac{N}{N_0}={\left(\frac{1}{2}\right)}^{t/40}$ or $\left(\frac{1}{4}\right)={\left(\frac{1}{2}\right)}^{t/40}$ or ${\left(\frac{1}{2}\right)}^2={\left(\frac{1}{2}\right)}^{t/40}$ Hence, $\frac{t}{40}=2$ or t = 80 year Decay constant $\lambda =\frac{0.693}{T_{1/2}}=\frac{0.693}{40}=0.0173year$