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

Question

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

Toppr Admin · Accepted Answer

Initial activity of the sample -xA0-Ro-9750 count-minActivity after t-5 min- -xA0-R-975 -xA0-count-minUsing First order decay- -xA0-R-Roe-x2212-x3BB-t-x2234- -xA0- 975-9750e-x2212-5-x3BB-Or -xA0-x2212-ln10-x2212-5-x3BB-Or -xA0-2-303-5-x3BB-x27F9- -xA0-x3BB-0-461 min-x2212-1

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

Initial activity of the sample Ro=9750 count/minActivity after t=5 min, R=975 count/minUsing First order decay, R=Roe−λt∴ 975=9750e−5λOr −ln10=−5λOr 2.303=5λ⟹ λ=0.461 min−1

Initial activity of the sample $R_{o} = 9750$ count/min
Activity after $t = 5$ min, $R = 975$ count/min
Using First order decay, $R = R_{o} e^{- λ t}$
$∴$ $975 = 9750 e^{- 5 λ}$
Or $- ln 10 = - 5 λ$
Or $2.303 = 5 λ$
$⟹$ $λ = 0.461$ $m i n^{- 1}$