A radioactive material P first decays into Q and then Q decays to non-radioactive material R. Which of the following figure represents time dependent mass of P, Q and R ?

Solution

Physics sir · 4 steps

Q is fed by P and also drains into R, so Q must rise, peak and then fall. Look for that hump.

1. Parent P. Nothing makes P, it only decays. Its mass falls exponentially from the start, m_P = m₀ e^(-λ_P t).
2. Daughter Q. Q starts at zero. Early on P is plentiful, so Q forms faster than it decays and its mass rises. Later P runs out but Q keeps decaying, so its mass passes through a maximum and then falls towards zero.
3. Final product R. R is stable, so it only collects and never decreases. It starts at zero, grows slowly at first because little Q exists yet, and levels off near the initial mass of P. Total mass stays fixed, so no curve can grow without limit.

   Option	P	Q	R	Fits?
   (a)	decays	rises and levels off	rises and levels off	no, Q never falls
   (b)	decays	rises, peaks, falls	rises from zero, keeps growing	yes
   (c)	decays	grows without limit	peaks, then falls	no, Q and R swapped
   (d)	decays	grows without limit	grows without limit	no, breaks mass conservation

4. So. Only (b) shows P falling, Q rising to a peak and then dying away, and R building up from zero. The answer is (b).

The idea to keep. In a chain P → Q → R: the parent only falls, a radioactive middle member always rises to a peak and then falls, and the stable end product only rises towards the starting mass.

Answer from the NTA final answer key. Solution by PrepWiser.