Question

Which differential equation correctly represents the above process?

• A. $\frac{dN}{dt}+\lambda N=q_{0}t$
• B. $\frac{dN}{dt}-\lambda N=q_{0}t$
• C. $\frac{dN}{dt}+q_{0}t=\lambda N$
• D. $\frac{dN}{dt}+q_{0}t=-\lambda N$

Answer 1

Answer: (A)

$\frac{dN}{dt}+\lambda N=q_{0}t$

At any time $q_{o}t$ radionuclide are produced and $\lambda N$ is the decay. Therefore,

$\frac{dN}{dt}=q_{o}t-\lambda N$

$\frac{dN}{dt}+\lambda N=q_{o}t$