Question
Hard
Solving time: 10 mins
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.
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Text solutionVerified
Given:
Resistance of resistor,
Inductance of an inductor,
Current (i) at any time (t) is given by
Number of active nuclei at any time (t) is given by
Where
Total number of nuclei
Disintegration constant
Now,
As is independent of time, coefficients of are equal.
Let be the half-life of the isotope.
Resistance of resistor,
Inductance of an inductor,
Current (i) at any time (t) is given by
Number of active nuclei at any time (t) is given by
Where
Total number of nuclei
Disintegration constant
Now,
As is independent of time, coefficients of are equal.
Let be the half-life of the isotope.
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Question Text | 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. |
Topic | Nuclei |
Subject | Physics |
Class | Class 12 |
Answer Type | Text solution:1 |
Upvotes | 60 |