Decay Constant — Prelims Questions

The half-life of a radioactive isotope is 20 days. What is its decay constant?

A radioactive sample has a decay constant of $0.01 \text{ s}^{-1}$. What fraction of the original sample will remain after 100 seconds?

Which of the following statements about the decay constant ($\lambda$) is correct?

If the decay constant of a radioactive substance is $\lambda$, what is the time taken for its activity to fall to $1/8$th of its initial value?

A radioactive sample contains $10^{20}$ nuclei initially. If its decay constant is $2.303 \times 10^{-2} \text{ s}^{-1}$, how many nuclei will remain after 100 seconds? (Given: $e^{-2.303} \approx 0.1$)

A radioactive substance has a mean life of 50 years. What is its half-life?