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 at t=0 and 975 count/ min at t=5 min. The decay constant is nearly (A)  0.922 min -1  (B)  0.691 min -1  (C) 0.461 min -1 (D)  0.230 min -1

Tardigrade Admin · Accepted Answer

Activity, A=A0 e-λ t ∴ 975=9750 e-λ × 5 (1/10)=e-λ × 5 Taking logarithm on both sides, we have - log e 10=-5 λ -2.3026=-5 λ λ=(2.3026/5)=0.461 min -1

Q. 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

$0.922 min^{- 1}$

$0.691 min^{- 1}$

$0.461 min^{- 1}$

$0.230 min^{- 1}$

Activity, $A = A_{0} e^{- λ t}$
$∴ 975 = 9750 e^{- λ \times 5}$
$\frac{1}{10} = e^{- λ \times 5}$
Taking logarithm on both sides, we have
$- lo g_{e} 10 = - 5 λ$
$- 2.3026 = - 5 λ$
$λ = \frac{2.3026}{5} = 0.461 mi n^{- 1}$

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

0.922min−1

0.691min−1

0.461min−1

0.230min−1