A spectral line of the Paschen series of hydrogen is observed at a wavelength of

CHEMISTRY · Subjective · CBSE · Chemistry · Structure of Atom · Structure of Atom

Problem

A spectral line of the Paschen series of hydrogen is observed at a wavelength of 1875 nm1875\,\text{nm}. (a) Show, by suitable calculation, the principal quantum number of the initial orbit from which the electron jumped to reach the Paschen series limit nf=3n_f=3. (b) Compute the energy of the emitted photon in electron-volt. (c) If the entire photon momentum is transferred to the hydrogen atom (mass 1.67×10−27 kg1.67\times10^{-27}\,\text{kg}), calculate the recoil kinetic energy acquired by the atom. Express your answer in eV and comment on how it compares with the photon energy.

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