In transient equilibrium, which statement is correct?

In transient equilibrium, which statement is correct?

• A. The daughter decays much slower than the parent but not greatly.
• B. They decay at the same rate.
• C. The parent decays faster than the daughter.
• D. The parent decays much slower than the daughter but not greatly.

Answer: (D)

Transient equilibrium happens when the daughter nucleus decays faster than the parent (shorter half-life), but not by a huge amount. The parent keeps feeding the daughter as it decays, so the production rate of the daughter can balance its own decay rate for a period of time. When dN_d/dt ≈ 0, the relation λ_p N_p ≈ λ_d N_d holds, which means the activities are about equal: A_p ≈ A_d. Since the parent has the longer half-life, it decays much more slowly than the daughter, but the separation of timescales isn’t extreme. That combination—a much slower-decaying parent and a faster-decaying daughter with nearly equal activities—is the essence of transient equilibrium.

Transient equilibrium happens when the daughter nucleus decays faster than the parent (shorter half-life), but not by a huge amount. The parent keeps feeding the daughter as it decays, so the production rate of the daughter can balance its own decay rate for a period of time. When dN_d/dt ≈ 0, the relation λ_p N_p ≈ λ_d N_d holds, which means the activities are about equal: A_p ≈ A_d. Since the parent has the longer half-life, it decays much more slowly than the daughter, but the separation of timescales isn’t extreme. That combination—a much slower-decaying parent and a faster-decaying daughter with nearly equal activities—is the essence of transient equilibrium.