Physics Concept Notes for JEE: Atoms
Review targeted revision notes for JEE Physics with the JEE Physics Atoms Notes Set 05. Built according to official educational guidelines for the 2026-27 academic year, these downloadable summaries for Atoms support daily study and last-minute exam readiness.
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Bohr Model of Hydrogen-like Atoms
Bohr assumed that the electron moves in certain circular orbits without radiating, that the angular momentum in these orbits is \( L=\frac{nh}{2\pi} \), and that a photon is emitted or absorbed only when the electron jumps between orbits, with \( h f=E_i-E_f \).
For a nucleus of charge Z (one electron), radius \( r_n=0.53\frac{n^2}{Z}\ \text{Å} \), speed \( v_n=2.19\times10^6\frac{Z}{n}\ \text{m/s} \) and energy \( E_n=-13.6\frac{Z^2}{n^2}\ \text{eV} \). The energy needed to remove the electron from level n is \( 13.6\frac{Z^2}{n^2} \) eV.
Spectral Lines
The wavelength of the line for a jump from \( n_i \) to \( n_f \) is given by \( \frac1\lambda=RZ^2\left(\frac1{n_f^2}-\frac1{n_i^2}\right) \), with \( R=1.097\times10^7\ \text{m}^{-1} \).
Lyman series ends on n = 1 (ultraviolet), Balmer on n = 2 (visible), Paschen on n = 3 (infrared). Remember that the ground state is n = 1, the first excited state is n = 2, and so on. A larger energy gap gives a shorter wavelength.
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