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