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A hydrogen atom initially at rest in the $n=3$ state decays to the ground state with the emission of a photon. (a) Calculate the wavelength of the emitted photon. (b) Estimate the recoil momentum of the atom and the kinetic energy of the recoiling atom. Where does this energy come from?

(a) $\lambda=102.57 \mathrm{nm}$

(b) $p=12.089 \mathrm{eV} / \mathrm{c}$ and $K=7.79 \times 10^{-8} \mathrm{eV}$.

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Indian Institute of Technology Kharagpur

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