First slide

Radio activity

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

Moderate

A

0.230 per minute
B

0.461 per minute
C

0.691 per minute
D

0.922 per minute

Solution

$A = A_{0} e^{- λt} \Rightarrow 975 = 9750 e^{- λx 5} \Rightarrow e^{5 λ} = 10 \Rightarrow 5 λ = \log_{e} 10 = 2.3026 \log_{10} 10 = 2.3026 \Rightarrow λ = 0.461$

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