Question

The activity of a radioactive sample is measured as 9750 counts per minute at t = 0 and as 975 counts per minute at t = 5 minutes. The decay constant is approximately.

• A. 0.230 per minute
• B. 0.461 per minute
• C. 0.691 per minute
• D. 0.922 per minute

Answer 1

Answer: (B)

0.461 per minute

Answer 2

$A = A_{0}e^{- \lambda t} \Rightarrow 975 = 9750\mspace{6mu} e^{- \lambda \times 5}$ $\Rightarrow e^{5\lambda} = 10$

$\Rightarrow 5\lambda = \log_{e}10 = 2.3026\log_{10}10 = 2.3026$

$\Rightarrow \lambda = 0.461$