A radioactive with decay constant `lambda` is being produced in a nuclear ractor at a rate `q_(0)` per second, where `q_(0)` is a positive constant and t is the time. During each decay, `E_(0)` energy is released. The production of radionuclide starts at time `t=0`.
Instantaneous power developed at time t due to the decay of the radionuclide is .

Options

A. (q_(0)t-q_(0)/(lambda)+q_(0)/(lambda)e^(-lambdat))E_(0)`
B. (q_(0)t+q_(0)/(lambda)-q_(0)/(lambda)e^(-lambdat))E_(0)`
C. (q_(0)t+q_(0)/(lambda)+q_(0)/(lambda)e^(-lambdat))E_(0)`
D. (q_(0)t+q_(0)/(lambda)-q_(0)/(lambda)e^(-lambdat))E_(0)`

Answer

a

Explanation

`N=(q_(0)t)/(lambda)-(q_(0))/(lambda^(2))+(q_(0))/(lambda^(2))e^(-lambdat)`
`P_(i nst)=lambdaNE_(0)=[q_(0)t-(q_(0))/(lambda)+(q_(0))/(lambda)e^(-lambdat)]E_(0)`.