Radioactive isotopes are produced in a nuclear physics experiment at a constant rate dN/dt = R. An inductor of inductance 100 mH, a resistor of resistance 100 Ω and a battery are connected to form a series circuit. The circuit is switched on at the instant the production of radioactive isotope starts. It is found that i/N remains constant in time where i is the current in the circuit at time t and N is the number of active nuclei at time t. Find the half-life of the isotope.
Given, Resistance R= 100Ω
Inductance L= 100mH
Let initial current be i˳
After time t,
Current at time t is given by
(where R is the resistance, L is the inductance)
So,
As the ratio should be independent of time,
∴