Which of the following expressions represents the spectrum...

Which of the following expressions represents the spectrum of Balmer series (If $\mathrm{n}$ is the ' principal quantum number of higher energy level) in Hydrogen atom ? (a) $\bar{v}=\frac{R(n-1)(n+1)}{n^{2}} \mathrm{~cm}^{-1}$ (b) $\bar{v}=\frac{R(n-2)(n+2)}{4 n^{2}} \mathrm{~cm}^{-1}$ (c) $\bar{v}=\frac{R(n-2)(n+2)}{n^{2}} \mathrm{~cm}^{-1}$ (d) $\bar{v}=\frac{R(n-1)(n+1)}{4 n^{2}} \mathrm{~cm}^{-1}$

Which of the following expressions represents the spectrum of Balmer series (If $\mathrm{n}$ is the ' principal quantum number of higher energy level) in Hydrogen atom ?
(a) $\bar{v}=\frac{R(n-1)(n+1)}{n^{2}} \mathrm{~cm}^{-1}$
(b) $\bar{v}=\frac{R(n-2)(n+2)}{4 n^{2}} \mathrm{~cm}^{-1}$
(c) $\bar{v}=\frac{R(n-2)(n+2)}{n^{2}} \mathrm{~cm}^{-1}$
(d) $\bar{v}=\frac{R(n-1)(n+1)}{4 n^{2}} \mathrm{~cm}^{-1}$

Key Concepts

Principal Quantum Number

The principal quantum number, denoted as n, defines the energy level of an electron in an atom. For the hydrogen spectrum, it uniquely identifies the initial and final states of an electron during transitions, which in turn determines the energy and wavelength of the emitted or absorbed photon.

Quantum Transitions

Quantum transitions refer to the movement of an electron from one energy level to another within an atom. In the context of the hydrogen atom, transitions to the n = 2 energy level produce the visible Balmer series, and the energy difference between the levels is directly related to the frequency or wavelength of the emitted light.

Balmer Series

The Balmer series is a set of spectral emission lines of the hydrogen atom that occur when electrons transition from higher energy levels (with principal quantum number n ? 3) down to the n = 2 level. This series is significant because it lies in the visible spectrum and was historically important in the development of quantum mechanics.

Rydberg Formula

The Rydberg formula is an equation used to predict the wavelengths (or wavenumbers) of light emitted by electrons as they transition between energy levels in a hydrogen atom. It is expressed in terms of the Rydberg constant and the inverse squares of the principal quantum numbers of the lower and higher energy levels.

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