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 Omega` 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.

Answer

A, C, D

Explanation

Given `(dN)/(dt) = R`
We know that `(dN)/(dt) = -lambdaN`
`rArr R = -lambdaN.`
Using given values
`lambda = 100`
So, required half life `= 0.693/lambda`
`= 0.693/100 = 6.93 xx 10^(-3)`.