Question

A radioactive element has rate of disintegration 10,000 disintegrations per minute at a particular instant. After four minutes it become 2500 disintegrations per minute. The decay constant per minute is ______.

Options

• 0.2 log_e 2

• 0.5 log_e 2

• 0.6 log_e 2

• 0.8 log_e 2

Answer 1

A radioactive element has rate of disintegration 10,000 disintegrations per minute at a particular instant. After four minutes it become 2500 disintegrations per minute. The decay constant per minute is 0.5 log_e 2.

Explanation:

According to question,

N₀ = 10,000 disintegration/min

N_t = 2500 disintegration/min

t = 4 min

From the radioactive decay law,

`"Nt"/"N"_0="e"^(-lambda"t")`

or, `2500/10000="e"^(-lambdaxx4)`

⇒ `1/4"e"^(-4lambda)`

⇒ `"e"^(4lambda)` = 4

⇒ 4λ = log_e 4 ⇒ 4λ = log_e 2²

⇒ 4λ = 2 log_e 2

∴ λ = 0.5 log_e 2