What is the maximum wavelength line in the Lyman series of He^+ ion? (a) 3 R (b) (1)/(3 R) (c) (

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What is the maximum wavelength line in the Lyman series of...

Key Concepts

Lyman Series

The Lyman series refers to the set of spectral lines in a hydrogen-like atom that are produced when electrons fall from higher energy levels to the ground state (n = 1). These transitions release energy, with each transition corresponding to a specific wavelength in the ultraviolet region of the electromagnetic spectrum.

Rydberg Formula

The Rydberg formula is used to calculate the wavelengths of the spectral lines emitted or absorbed by hydrogen-like atoms. It relates the inverse of the wavelength (wavenumber) to the difference of the inverses of the squares of the principal quantum numbers, with a scaling factor known as the Rydberg constant. For hydrogen-like ions, the formula is modified by including the square of the atomic number (Z²), reflecting the increased nuclear charge.

Hydrogen-like Ions

Hydrogen-like ions are atoms that have a single electron, similar to a hydrogen atom, but with a higher nuclear charge (Z > 1). In these ions, the energy levels and corresponding spectral transitions are affected by the increased attraction between the nucleus and the electron, and this is accounted for in the Rydberg formula by the Z² factor.

Emission Line Wavelengths

The wavelength of an emission line is determined by the energy difference between the initial and final electron energy levels. In a series like the Lyman series, the maximum wavelength corresponds to the smallest energy gap, which is generally the transition from n = 2 to n = 1, as it involves the minimum difference in energy between allowed levels.

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