Savchenko Problem 14.5.19

PART A

This is about conservation of momentum and mass-energy in nuclear decay. When the excited nucleus emits a photon and comes to rest, all its initial momentum must equal the photon's momentum—use $p_{\text{nucleus}} = p_{\gamma}$ to find the starting speed. The mass difference between excited and ground states equals the photon's energy divided by $c^2$, since that energy came from converting mass.

PART B

For absorption to occur, the moving excited nucleus must emit a photon with just enough energy to be absorbed by a stationary nucleus—but recoil makes this tricky. The key insight is that the emitted photon's energy depends on the nucleus's velocity (Doppler shift), so there's a specific velocity range where the photon energy matches the absorption requirement of the stationary nucleus.

PART A

This is about conservation of momentum and mass-energy in nuclear decay. When the excited nucleus emits a photon and comes to rest, all its initial momentum must equal the photon's momentum—use $p_{\text{nucleus}} = p_{\gamma}$ to find the starting speed. The mass difference between excited and ground states equals the photon's energy divided by $c^2$, since that energy came from converting mass.

PART B

For absorption to occur, the moving excited nucleus must emit a photon with just enough energy to be absorbed by a stationary nucleus—but recoil makes this tricky. The key insight is that the emitted photon's energy depends on the nucleus's velocity (Doppler shift), so there's a specific velocity range where the photon energy matches the absorption requirement of the stationary nucleus.