Question

The relation between half life (T) and decay constant () is

A
λT=1
B
λT=12
C
λT=loge2
D
λ=log2T
Solution
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The correct option is C λT=loge2
As per radiaoactive decay law, the radioactive decays per unit time are directly proportional to the total number of nuclei of radioactive compounds in the sample.
f the number of nuclei in a sample is N and the number of radioactive decays per unit time dt is dN then,
dNdt=λN
Integrating both limits
NN0dNN=λ tt0dt
Taking initial time t0=0 we have

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