Question

Open in App

Updated on : 2022-09-05

Solution

Verified by Toppr

Correct option is D)

According to question, at $t=5$ $min$

$N=eN_{o} $

Therefore, equation of nuclei left undecayed after time, $t$ is given by,

$N=N_{o}(21 )_{t/T_{1/2}}$

when $t=5$ $min$, $N=eN_{o} $

$⟹eN_{o} =N_{o}(21 )_{5/T_{1/2}}$

$⟹e_{−1}=(21 )_{5/T_{1/2}}$

Calling log both sides,

$⟹−ln(e)=T_{1/2}5 ln(21 )$

And as we know $ln(e)=1$

$⟹T_{1/2}=−5ln(1/2)$

$⟹T_{1/2}=−5(−ln2)$

$⟹T_{1/2}=5ln2$

$⟹T_{1/2}=5g_{e}2$

Was this answer helpful?

0

0