Question

Half life period of a radioactive sample is T. Let
x fraction disintegrates in time 't'. How much
fraction will decay in
time t/2​

Answer 1

Half life period of a radioactive sample is T.

• Now, we know the decay law gives,
•                         N = N₀e^(-kt₁)
• Where, N = Present amount of sample
• N₀ = Initial amount of sample
• k = decay constant
• t₁ = time taken
• Now t1 =t gives N/N₀ = (1-x) since x is the fraction decayed
• For, t1 = t/2 We have

                  N/N₀ = e^(-kt)

or,              (N/N₀)^(1/2) = e^(-kt/2)

or,              (1-x)^1/2 = (N/N₀)^1/2

• Hence, the fraction that will decay in time t/2 is 1 -(1-x)^1/2