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प्रश्न
A certain sample of a radioactive material decays at the rate of 500 per second at a certain time. The count rate falls to 200 per second after 50 minutes. (a) What is the decay constant of the sample? (b) What is its half-life?
उत्तर
Given:-
Initial rate of decay, A0 = 500,
Rate of decay after 50 minutes, A = 200
Time, t = 50 min
= 50 × 60
= 3000 s
(a)
Activity, A = A0e−λt
Here, `lambda` = Disintegration constant
`therefore 200 = 500 xx e^(-50 xx 60 xx lambda)`
`⇒ 2/5 = e^(-3000lambda)`
`⇒ "In" 2/5 = -3000lambda`
`⇒ lambda = 3.05 xx 10^-4 "s"^-1`
(b)
Half - life, `T_"1/2" = 0.693/lambda`
`= 2272.13 "s"`
= 38 min
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