Question

The disintegration rate of a certain radioactive sample at any instant is $4250$ disintegrations per minute. $10$ minutes later, the rate becomes $2250 $ disintegrations per minute. The approximate decay constant is : (Take $\log _{10} 1.88=0.274$ )

• A. $0.02 \,\min ^{-1}$
• B. $2.7 \,\min ^{-1}$
• C. $0.063 \,\min ^{-1}$
• D. $6.3 \,\min ^{-1}$

Answer 1

Answer: (C)

At $t =0 $ disintegration rate $=4250\, dpm$
At $t =10$ disintegration rate $=2250 \,dpm$
$A=A_o e^{-\lambda t}$
$ 2250=4250 e ^{-\lambda(10)}$
$ \Rightarrow \lambda(10)=\ln \left(\frac{4250}{2250}\right) $
$ \Rightarrow \lambda=0.063 \,\min ^{-1}$