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A proton strikes a stationary deuteron to form a He-3 nucleus. For this reaction to occur, the proton must carry a minimum kinetic energy of 1.4 MeV. If the roles are reversed and a deuteron strikes a stationary proton (to form the same He-3 nucleus), what is the minimum kinetic energy the deuteron must possess?

1. 0.7 MeV
2. 1.4 MeV
3. 2.8 MeV
4. 4.2 MeV

Correct answer: 2.8 MeV

Solution

The CM-frame threshold energy is fixed by the Q-value. For a projectile of mass m hitting a target of mass M at rest, E_th = E_cm * (m+M)/(2M). With proton (mass 1u) on deuteron (mass 2u): E_th = E_cm * 3/4. With deuteron (mass 2u) on proton (mass 1u): E_th = E_cm * 3/2. The ratio of the two thresholds is (3/2)/(3/4) = 2, so deuteron threshold = 2 * 1.4 = 2.8 MeV.

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