JEE Main 2022 · 28 June · morning · Single correct · +4 / −1
The Q-value of a nuclear reaction and kinetic energy of the projectile particle, Kₚ are related as :
- (a) Q = Kₚ
- (b) (Kₚ + Q) < 0
- (c) Q < Kₚ
- (d) (Kₚ + Q) > 0
Answer and solution
Answer (d) (Kₚ + Q) > 0
Solution
Physics sir · 4 steps
Do the energy bookkeeping: what comes out as kinetic energy is Kₚ + Q, and that can never be negative.
- Define Q. The Q-value is the rest-mass energy released in the reaction: Q = (mᵢₙᵢₜᵢₐₗ - m_(final))c². A positive Q means mass turns into kinetic energy. A negative Q means kinetic energy must be used up to create mass.
- Energy conservation. Take the target at rest, so the only kinetic energy going in is the projectile's Kₚ. Total energy is conserved, so the kinetic energy of the products is the incoming kinetic energy plus the energy released.
K_(products) = Kₚ + Q
- Products must move. Kinetic energy is never negative. The products also carry the projectile's momentum, so they cannot all end up at rest, which makes K_(products) strictly positive.
- So. For any reaction that actually happens, (Kₚ + Q) > 0. That is option (d).
The idea to keep. In any nuclear reaction, kinetic energy out = kinetic energy in + Q. Since products always carry kinetic energy, Kₚ + Q must be positive. For negative Q, the projectile has to supply the deficit.
Answer from the NTA final answer key. Solution by PrepWiser.