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Q.

A point-like radioactive sample of decay constant λ initially at a distance r0  from a radiation counter starts  moving towards the counter. If the count rate recorded by the counter remains constant with time, then speed  of the radioactive sample as function of time is  v=λr0ae−λtb.Find product  ab? (Assume radiation spreads equally in space)

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Detailed Solution

Count rate recorded by the counter at any time ‘t’ is  λN4πr2A where ‘N’  is number of undecayed Nuclei, ‘r’  is the separation between sample and counter.  A is the area of counter.Since rate recorded is constant  λN4πr2A=λN04πr02A ⇒r2=r02e-λt ⇒r=r0e−λt2 . Speed  v=|drdt|=v=λr02e−λt2
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