Question

A count rate-meter is used to measure the activity of a given sample. At one instant the meter shows $4750$ counts per minute. Five minutes later it shows $2700$ counts per minute. The decay constant of the sample is

• A. 0.565 min${}^{-1}$
• B. 0.452 min${}^{-1}$
• C. 0.226 min${}^{-1}$
• D. 0.113 min${}^{-1}$

Answer 1

The correct option is D 0.113 min${}^{-1}$

From general law of rate of reactions, $N=N_o{e}^{-\lambda t}$

$\Rightarrow 2700=4750e^{-\lambda 5}\Rightarrow ln\left(\frac{270}{475}\right)=-\lambda 5$

$\Rightarrow \lambda =0.1129\approx 0.113mi{n}^{-1}$