1.

The counting rate observed from the radioactive source at t= 0 second was 1600 counts/sec and t= 8 sec, it was 100 count/sec. The counting rate per sec at t =6 sec will be:

Answer»

400
300
200
150

Solution :`(d N)/(dt)=LAMBDA N, =lambda N_(0) E^(-lambda t)`
1ST CASE: when t=0, 1600/sec `=lambda N_(0)`
2nd case: when t=8sec. `(d N)/(dt)=lambda N_(0) e^(-8lambda)`
`or 100 =lambda N_(0) e^(-8lambda) =1600 e^(-8 lambda)`
`or 1/(16) =e^(-8lambda) or (1/2)^(4)=(e^(-2 lambda)^(4)`
`e^(-2lambda)=1/2`
3rd case" t=6 sec
`(d N)/(dt)=1600 e^(-6 lambda)=1600 (e^(-2lambda))^(3)`
`=1600 xx (1/2)^(3)=1600 xx 1/8 =200//sec`.


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