In secular equilibrium, what is true about the decay rates?

In secular equilibrium, what is true about the decay rates?

• A. They decay at the same rate.
• B. The parent decays much slower than the daughter.
• C. The daughter decays much slower than the parent.
• D. The parent decays faster than the daughter.

Answer: (B)

In secular equilibrium, the parent is long-lived while the daughter is short-lived, so the decay constant for the parent is much smaller than that of the daughter. The ongoing production of the daughter from the parent quickly builds up a steady-state population whose own decay matches the parent’s decay rate. As a result, the two decay rates become equal in magnitude, but the parent itself decays far more slowly than the daughter because its half-life is much longer. This is why the statement that the parent decays much slower than the daughter best describes secular equilibrium.

In secular equilibrium, the parent is long-lived while the daughter is short-lived, so the decay constant for the parent is much smaller than that of the daughter. The ongoing production of the daughter from the parent quickly builds up a steady-state population whose own decay matches the parent’s decay rate. As a result, the two decay rates become equal in magnitude, but the parent itself decays far more slowly than the daughter because its half-life is much longer. This is why the statement that the parent decays much slower than the daughter best describes secular equilibrium.