An excited nucleus of mass approximately 100 u emits a γ-photon of energy 2.0 MeV and was initially at rest. Take 1 u·c² = 931.5 MeV. Using the non-relativistic recoil approximation, find the recoil kinetic energy of the daughter nucleus in eV, rounded to the nearest integer.
Physics · Nuclear physics · radioactivity and law of decay
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Question

An excited nucleus of mass approximately 100 u emits a γ-photon of energy 2.0 MeV and was initially at rest. Take 1 u·c² = 931.5 MeV. Using the non-relativistic recoil approximation, find the recoil kinetic energy of the daughter nucleus in eV, rounded to the nearest integer.

Physics · Nuclear physics · radioactivity and law of decay

G1 Physics · Accepted Answer

The photon momentum is p(γ) = E(γ) ÷ c. Momentum conservation gives the daughter nucleus the same momentum magnitude. Its recoil kinetic energy is K(R) = p² ÷ (2M) = E(γ)² ÷ [2Mc²]. For M ≈ 100u: Mc² = 100×931.5 = 93150 MeV. Thus, K(R) = 2.0² ÷ [2×93150] MeV = 4 ÷ 186300 MeV ≈ 2.147×10⁻⁵ MeV. Convert MeV to eV: K(R) ≈ 2.147×10⁻⁵×10⁶ ≈ 21.47 eV. Nearest integer = 21. Hence N = 21.