Question

Calculate the time required for 60% of a sample of radon to undergo decay. Given T_1/2 of radon = 3.8 days.

Answer 1

Half life of radon = 3.8 days

Amount of sample disintegrated = 60%

Time required =?

λ = `0.6931/3.8` per day

Amount of sample disintegrated = 60%

Amount of sample present = 40%

Let N₀ be the original amount of the sample present.

From law of disintegration,

N = N₀ e^-λt

Substituting N = 40% of N₀,

`(40/100)` N₀ = N₀ e^-λt

e^-λt = `(40/100)`

e^-λt = `40/100`

e^-λt = `(100/40)` = 2.5

Log e 2.5 = λ × t

t = `(log_10 2.5 xx 2.3026 xx 3.8)/0.6931`

t = 5.022 days