Define the Activity of a radioactive sample. Write its S.I. unit. A radioactive sample has activity of 10000 disintegrations per second (dps) after 20 hours. After next 10 hours its Activity reduces to 5000 dps. Find out its half-life and initial activity.

Explanation

1st part : The activity of a radioactive sample is defined as the rate of disintegration of the sample. It is also called count rate.
Its SI unit is becquerel (Bq).
1Bq= 1 decay/s
2nd part : We know , `A=A_0e^(-lambdat)`
or, `5000 = 10000 e^(-lambdat)` or , `e^(lambdat) =10000/5000=2`
Taking log on both sides , we get
`lambdat = log 2 ` or , `lambda="log 2 "/t`
Now , half life , `T=0.693/lambda=(0.693xxt)/(log 2) =(0.693xx600)/(log 2)`
=1381.26 min `~~` 23 h
Now ,
In this table, the last two values ae the given values . From these values, the first two values have been calculated .
Hence, the initial activity is 40000 dps .