Question

The activity of a radioactive sample is measured as 9750 count/min at t = 0 and 975 count/min at t = 5 min.The decay constant is nearly

• A. 0.922 $mi{n}^{-1}$
• B. 0.691 $mi{n}^{-1}$
• C. 0.461 $mi{n}^{-1}$
• D. 0.230 $mi{n}^{-1}$

Answer 1

Answer: (C)

0.461 $mi{n}^{-1}$

Initial activity of the sample $R_o=9750$ count/min

Activity after $t=5$ min, $R=975$ count/min

Using First order decay, $R=R_o{e}^{-\lambda t}$

$\therefore$ $975=9750e^{-5\lambda }$

Or $-\ln 10=-5\lambda$

Or $2.303=5\lambda$

$⟹$ $\lambda =0.461$ $mi{n}^{-1}$