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Grade 12Physical Chemistry

41Ar is a radioisotope used to measure the flow of gases from smoke chimneys. A sample
of 41Ar decays initially at a rate of 32500 disintegrations/minute. The decay falls to 24500
disintegrations/minute after 75 min. The half-life of the isotope

Punit Sinha

8 Years agoGrade 12

1 Answer

Eshan

8 Years ago

Dear student,

Rate of disintegration at some time is given as
$\dfrac{dN}{dt}=-\lambda N$

Hence $\dfrac{N}{N_0}=\dfrac{(\dfrac{dN}{dt})_t}{(\dfrac{dN}{dt})_0}=\dfrac{24500}{32500}=\dfrac{49}{65}$

Also we know that $N=N_0e^{-\lambda t}$
$\implies \lambda t=ln(\dfrac{N_0}{N})=ln(\dfrac{65}{49})=\lambda (75)$
$\implies \lambda =0.00376min^{-1}$
Hence half life= $t_{1/2}=\dfrac{ln 2}{\lambda}=184min$

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