For the Balmer series in the spectrum of H atom, v̅=RH{(1)/(n1^2)-(1)/(n2^2)}, the correct state

Step 1:u000AThe Balmer series is a series of lines in the spectrum of the hydrogen atom which corres

For the Balmer series in the spectrum of H atom,...

For the Balmer series in the spectrum of $\mathrm{H}$ atom, $\bar{v}=R_{H}\left\{\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right\}$, the correct statements among (I) to (IV) are: (I) As wavelength decreases, the lines in the series converge (II) The integer $n_{1}$ is equal to 2 (III)The lines of longest wavelength corresponds to $n_{2}=3$ (IV) The ionization energy of hydrogen can be calculated from wave number of these lines (a) (I), (III), (IV) (b) (I), (II), (III) (c) (I), (II), (IV) (d) (II), (III), (IV)

For the Balmer series in the spectrum of $\mathrm{H}$ atom, $\bar{v}=R_{H}\left\{\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right\}$, the correct statements among (I) to (IV) are:
(I) As wavelength decreases, the lines in the series converge
(II) The integer $n_{1}$ is equal to 2
(III)The lines of longest wavelength corresponds to $n_{2}=3$
(IV) The ionization energy of hydrogen can be calculated from wave number of these lines
(a) (I), (III), (IV)
(b) (I), (II), (III)
(c) (I), (II), (IV)
(d) (II), (III), (IV)

Key Concepts

Series Convergence

As the upper energy level (n2) increases, the difference in energy between successive levels decreases, causing the wavelengths (or wavenumbers) of the corresponding spectral lines to converge towards a limit. This convergence is an important feature in understanding the pattern of the spectral series.

Quantum Numbers

Quantum numbers label the energy levels of electrons in atoms. In the context of the Balmer series, the lower quantum number is fixed at n = 2, while the upper quantum number, n2, varies. This variation determines the energy difference between levels and thus the wavelength of the emitted light.

Ionization Energy

Ionization energy is the energy required to remove an electron completely from an atom, typically measured from the ground state (n = 1). While spectral lines provide insight into energy level transitions, care must be taken because series like the Balmer series (which involve transitions from n = 2) do not directly yield the ionization energy from the ground state without additional information.

Rydberg Formula

The Rydberg formula expresses the wavelength (or wavenumber) of spectral lines as a function of transitions between quantized energy levels in hydrogen-like atoms. It highlights the inverse-square dependency on quantum numbers and is foundational in explaining atomic spectra.

Balmer Series

The Balmer series is a set of spectral lines corresponding to transitions from higher energy levels down to the n = 2 level in a hydrogen atom. This series falls in the visible region of the electromagnetic spectrum and is characterized by the fixed lower quantum number, n1 = 2.

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