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The activity of a radioactive substance ...

The activity of a radioactive substance is `R_(0)` at `t = 0`, `R_(1)` at `t = t` and `R_(2)` at `t = 2t`. The decay constant of this species is/are given by:

A

`(log_(e) R_(1) - log_(e) R_(2))/(t)`

B

`(log_(e) R_(0) - log_(e) R_(1))/(t)`

C

`(log_(e) R_(2) - log_(e) R_(1))/(2t)`

D

`(log_(e) R_(0) - log_(e) R_(1))/(2t_(2))`

Text Solution

Verified by Experts

The correct Answer is:
`(a,b,d)`
`R_(1) = R_(0) e^(-lambda t)`
`R_(2) = R_(0) e^(-lambda 2t)`
`:. (R_(1))/(R_(2)) = e^(-lambda t)`
or `lambda = (log_(e) R_(1) - log_(e) R_(2))/(t)`
Similarly, `lambda = (log_(e) R_(0) - log_(e) R_(1))/(t)`
`lambda =(log_(e) R_(0) - log_(e) R_(2))/(2t)`
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