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A sample of 37Ar undergoes 8540disintegrations/min initially but undergoes 6990disintegrations/min after 10.0 days. What is the...

A sample of 37Ar undergoes 8540disintegrations/min initially but undergoes 6990disintegrations/min after 10.0 days. What is the half-life of 37Ar in days?

t 1/2= ? days

Solutions

Expert Solution

Since radio active component decays as first order

Let C be the concentration of radioactive compound then rate of decay is following ( let k be the rate constant )

dC/dt = ( - k ) ( C )

dC/C = ( - k ) dt

ln( C/C0 ) = ( - k )t                    ( Let C0 be the initial concentration )

( -k ) = ln( C/C0 ) / t

( - k ) = [ ( ln ( 1/2 ) ] / [ t1/2 ]                ( for half concentration t = t1/2 and concentration                                                                          become half so c = 1/2 C0 and t = t1/2)

k = ln2/t1/2

t1/2 = ln2/k

queen_honey_blossom answered 4 months ago
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