1. The problem statement, all variables and given/known data When a photon is emitted by an atom, the atom must recoil to conserve momentum. This means that the photon and the recoiling atom share the transition energy. (a) For an atom with mass m, calculate the correction Δλ due to recoil to the wavelength of an emitted photon. Let λ be the wavelength of the photon if recoil is not taken into consideration. (Hint: The correction is very small, so use this fact to obtain an approximate but very accurate expression for Δλ.) 2. Relevant equations 3. The attempt at a solution E = energy of system E' = energy of the photon K = kinetic energy of the atom Conservation of energy gives: Einitial = Efinal 0 = K + E' 0.5 x mv² = - (hc / λ) By conservation of momentum: 0 = pphoton + patom mv = - (h / λ) Solving the above equations, we get: λ = h / 2mc The book's answer is h / 2mc. The problem is that the speed found here is twice greater than c.