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 $