The wavelength of the first line of the He^+ ion spectral series whose interval between the extr

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The wavelength of the first line of the He^+ ion spectral...

The wavelength of the first line of the $\mathrm{He}^{+}$ ion spectral series whose interval between the extreme lines is $2.725 \times 10^{6} \mathrm{~m}^{-1}$ is $\left(R=1.09 \times 10^{7} \mathrm{~m}^{-1}\right)$ (a) $471.82 \mathrm{~nm}$ (b) $4718.2 \mathrm{~nm}$ (c) $1019.37 \mathrm{~nm}$ (d) $165.14 \mathrm{~nm}$

The wavelength of the first line of the $\mathrm{He}^{+}$ ion spectral series whose interval between the extreme lines is $2.725 \times 10^{6} \mathrm{~m}^{-1}$ is $\left(R=1.09 \times 10^{7} \mathrm{~m}^{-1}\right)$
(a) $471.82 \mathrm{~nm}$
(b) $4718.2 \mathrm{~nm}$
(c) $1019.37 \mathrm{~nm}$
(d) $165.14 \mathrm{~nm}$

Key Concepts

Energy Level Transitions

Energy level transitions refer to the changes in the electron's energy state within an atom or ion, whereby electrons absorb or emit photons corresponding to the precise energy difference between levels. This concept is critical in understanding how spectral lines are produced and in calculating their wavelengths using formulas like the Rydberg equation.

Spectral Series

A spectral series is a set of related spectral lines resulting from electron transitions between a common lower energy level and various higher energy levels. Each series, such as those observed in hydrogen or hydrogen-like ions, displays a characteristic pattern that can be used to identify the line series and to determine missing parameters like the wavelength of a particular transition.

Hydrogen-like Ions

Hydrogen-like ions are species that have only one electron, similar to the hydrogen atom, but with a nucleus of higher charge. This increased nuclear charge modifies the energy levels relative to hydrogen, which is accounted for by adjusting the Rydberg constant, making the analysis of their spectral lines analogous but not identical to that of hydrogen.

Rydberg Formula

The Rydberg formula is fundamental in spectroscopy for calculating the wavelengths of emitted or absorbed light in atoms and ions. It relates the reciprocal of the wavelength to the difference between the squares of the reciprocals of two quantum numbers, multiplied by the Rydberg constant.

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