Passage A radio nuclide with decay constant \( \lambda \) is produced in a nuclear reactor at a ....
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A radio nuclide with decay constant \( \lambda \) is produced in a
\( \mathrm{P} \)
nuclear reactor at a rate \( \mathrm{q}_{0} t \) per second, where \( \mathrm{q}_{0} \) is constant and \( t \) is time. During each decay energy \( E_{0} \) is released. If at \( t=0 \), production of radio nuclide started, find
Which differential equation correctly represent the above process?
(1) \( \frac{\mathrm{dN}}{\mathrm{dt}}+\lambda \mathrm{N}=\mathrm{q}_{0} \mathrm{t} \)
(2) \( \frac{d N}{d t}-\lambda N=q_{0} t \)
(3) \( \frac{\mathrm{dN}}{\mathrm{dt}}+\mathrm{q}_{0} \mathrm{t}=\lambda \mathrm{N} \)
(4) \( \frac{d N}{d t}+q_{0} t=-\lambda N \)
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