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 log101.88 = 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)

0.063 min–1

Answer 2

$A_0=4250$
$A=2250$
$A=A_0e^{−λt}$
$2250=4250e−λt$
$\frac {2250}{4250}=e^{−λt}$
$λ(10)=ln (\frac {4250}{2250})$
$λ(10)=0.636$
$λ=0.063$

So, the correct option is (C): $0.063\ min^{-1}$