A radioactive isotope is being produced at a constant rate dN/dt = R in an experiment. The isotope has a half-life, t_1/2. After a time t t_1/2, the number of active nuclei will become constant. Th

Question

A radioactive isotope is being produced at a constant rate dN/dt = R in an experiment. The isotope has a half-life, t_1/2. After a time t >> t_1/2, the number of active nuclei will become constant. The value of this constant is

Prashant Kotian · Accepted Answer

Correct answer: C. The net rate of change of the isotope is: dN/dt = R - λ * N. At steady state (t >> t_1/2), the rate of change becomes zero (dN/dt = 0): 0 = R - λ * N -> N = R / λ.

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