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# The activity of a radioactive sample is measured as N0 counts per minute at t=0 and N0/e counts per minute at t=5 min. The time, (in minute) at which the activity reduces to half its value, is :loge255loge25log1025loge2

A
5loge2
B
5loge2
C
loge25
D
5log102
Solution
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#### Using first order equation N=Noe−λtGiven : N=Noe @ t=5 min∴Noe=Noe−λ(5)Or −logee=−5λ⟹λ=15(∵logee=1)Time at which the activity reduces to half of its initial value is known as half life of the radioactive substance.Half life T1/2=loge2λ=5loge2

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