A radioactive with decay constant `lambda` is being produced in a nuclear reactor 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`.
Which differential equation correctly represents the above process?.

Options

A. `(dN)/(dt)+lambda N=q_(0) t`
B. `(dN)/(dt)-lambda N=q_(0) t`
C. `(dN)/(dt)+q_(0) t=lambda N`
D. `(dN)/(dt)+q_(0) t=-lambda N`

Answer

A

Explanation

`(dN)/(dt)=q_(0) t-lambda N,(dN)/(dt)+lambda N=q_(0) t` .