A radioactive sample at any instant has its disintegration rate 5000 disintegrations per minute. After 5 min, the rate becomes 1250 disintegration per minute. Then, its decay constant (per minute) is

Question

A radioactive sample at any instant has its disintegration rate 5000 disintegrations per minute. After 5 min, the rate becomes 1250 disintegration per minute. Then, its decay constant (per minute) is (A)  0.8 log e2  (B)  0.4 log e2  (C)  0.2 log e2  (D)  0.1 log e2

Tardigrade Admin · Accepted Answer

Given R = 1250, R0=5000 and t = 5 min Hence R=R0e-λ t 1250=5000e-λ × 5 λ =0.4 log e2

Q. A radioactive sample at any instant has its disintegration rate $5000$ disintegrations per minute. After $5 min$ , the rate becomes $1250$ disintegration per minute. Then, its decay constant (per minute) is

$0.8 lo g_{e} 2$

$0.4 lo g_{e} 2$

$0.2 lo g_{e} 2$

$0.1 lo g_{e} 2$

$0.6 lo g_{e} 2$

Given R = 1250,
$R_{0} = 5000$ and t = 5 min
Hence $R = R_{0} e^{- λ t}$
$1250 = 5000 e^{- λ \times 5}$
$λ = 0.4 lo g_{e} 2$

Q. A radioactive sample at any instant has its disintegration rate 5000 disintegrations per minute. After 5min, the rate becomes 1250 disintegration per minute. Then, its decay constant (per minute) is

0.8loge​2

0.4loge​2

0.2loge​2

0.1loge​2

0.6loge​2

Given R = 1250, R0​=5000 and t = 5 min Hence R=R0​e−λt 1250=5000e−λ×5 λ=0.4loge​2