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Updated on : 2022-09-05

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Since from the graph; we have

$N=N_{−}e_{−λt}$ ....1

where $λ$=Disintegration constant

For $∴$ For $T_{1/2}$ is the time at $N−21 N_{D}$

$⇒$ $t=T_{1/2}$

$2N_{0} $=$N_{0}e_{−λ2T}$

$⇒$ $T_{1/2}=λLn2 =λ0.693 $

And for Mean life -we have to sum it over the whole Range for

$N(t)=N_{0}e_{−λt}$

for number of nuclei which decay in time t to t t $△$;

$N(t)△t=λN_{0}e_{−λt}△t$

For Integration it over the Range $T=0to∞$

$τ$=$N_{0}λN_{0}∬_{0}te_{−λt}dt $

$=λ∫_{0}te_{λt}dt$

$τ=λ1 $

Mean-life

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