The activity of a radioactive sample is measured as 9750 counts per minute at t=0 and as 975 counts per minute at t=5 minutes. The decay constant is approximately,

Question

The activity of a radioactive sample is measured as 9750 counts per minute at t=0 and as 975 counts per minute at t=5 minutes. The decay constant is approximately, (A) 0.922 per minute. (B) 0.691 per minute. (C) 0.461 per minute. (D) 0.230 per minute.

Tardigrade Admin · Accepted Answer

According to radioactivity decay law, the number of decays per second is directly proportional to the number of active samples.

\frac{d N}{d t} = λ N

9750 = λ N_{0}

.... (i)

975 = λ N

.... (ii)
Dividing (i) by (ii),

\frac{N}{N _{0}} = \frac{1}{10}

.
We know that,

λ = \frac{2.303}{t} l o g \frac{N _{0}}{N}

= \frac{2.303}{5} l o g 10

= 0.4606 = 0.461

per minute.

Q. The activity of a radioactive sample is measured as $9750$ counts per minute at $t = 0$ and as $975$ counts per minute at $t = 5$ minutes. The decay constant is approximately,

$0.922$ per minute.

$0.691$ per minute.

$0.461$ per minute.

$0.230$ per minute.

Q. The activity of a radioactive sample is measured as 9750 counts per minute at t=0 and as 975 counts per minute at t=5 minutes. The decay constant is approximately,

0.922 per minute.

0.691 per minute.

0.461 per minute.

0.230 per minute.

Q. The activity of a radioactive sample is measured as $9750$ counts per minute at $t = 0$ and as $975$ counts per minute at $t = 5$ minutes. The decay constant is approximately,

$0.922$ per minute.

$0.691$ per minute.

$0.461$ per minute.

$0.230$ per minute.