JEE Physics 2025 Question with Solution

Given: A radioactive material $P$ decays into $Q$, and then $Q$ decays into non-radioactive material $R$.

Find: The correct graph showing the time-dependent masses of $P$, $Q$ and $R$.

For the first decay,

So the mass of $P$ decreases exponentially with time.

For the intermediate product,

Thus $Q$ is first produced from $P$, so its mass initially increases, and later it decreases because it also decays into $R$.

The mass of $R$ is

Hence the mass of $R$ increases with time.

Therefore, the correct figure must show:

• $P$ decreasing continuously,
• $Q$ increasing first and then decreasing,
• $R$ increasing with time.

This behavior matches option (2).

Therefore, the correct option is B.

Given: $P \to Q \to R$, where $R$ is non-radioactive.

Find: Which graph correctly represents the masses of $P$, $Q$ and $R$ as functions of time.

1. Since $P$ is the original radioactive material, its mass must decrease with time.
2. Since $Q$ is formed from $P$ and also decays further, its mass cannot only increase or only decrease. It must first increase and then decrease.
3. Since $R$ is the final non-radioactive product, its mass keeps increasing as more decay occurs.

Checking the figures, only option (2) shows:

• a decreasing curve for $P$,
• a hump-shaped curve for $Q$,
• an increasing curve for $R$.

Therefore, the correct option is B.