Given:
Resistance of resistor, R = 100 Ω
Inductance of an inductor, L = 100 mH
Current at any time is given by
Number of active nuclei at any time is given by
Where N0 = Total number of nuclei
= Disintegration constant
Now,
As is independent of time, coefficients of t are equal.
Let be the half-life of the isotope.