The rate of decay of a radioactive sampel is given by `R_(1)` at time `t_(1)` and `R_(2)` at a later time. `t_(2)`. The mean life of this radioactive sample is:

Options

A. `T = (R_(1))/(R_(2)) xx (t_(2))/(t_(1))`
B. `T = (t_(1) - t_(2))/(In (R_(2) // R_(1)))`
C. `T = (t_(2) - t_(1))/(In (R_(2)//R_(1)))`
D. `T = (In (R_(2)//R_(1)))/(t_(1) - t_(2))`

Answer

b

Explanation

`R_(2) = R_(0) e^(-lambda t_(1))`
`R_(1) = R_(0) e^(-lambda t_(1))`
On dividing the above equation, we get
`(R_(2))/(R_(1)) = e^(lambda(t_(1) - t_(2)))`
In `((R_(2))/(R_(1))) - lambda (t_(1) - t_(2))`
`(1)/(lambda) = ((t_(1) - t_(2)))/(In (R_(2) // R_(1)))`
`T = ((t_(1) - t_(2)))/(In (R_(2)//R_(1)))`