The wavelength of radiation emitted out in the transition n=4 to n=1 in Li^2+ ion is (a) (135 R)

step 1 In the equation, we are going to find the wavelength of the radiation and that is 1 by lambda is

The wavelength of radiation emitted out in the transition...

Key Concepts

Hydrogen?like Ions

Hydrogen?like ions are atoms or ions that contain only one electron, so their electronic energy levels resemble the hydrogen atom but are affected by the nuclear charge. The structure of these energy levels is influenced by the charge of the nucleus, which alters the potential energy experienced by the electron.

Rydberg Formula

The Rydberg formula expresses the reciprocal of the wavelength of light emitted or absorbed during an electron transition between energy levels. It relates the difference between the inverse squares of the principal quantum numbers to a constant (the Rydberg constant) multiplied by the square of the nuclear charge in hydrogen?like ions, thereby predicting spectral lines.

Energy Level Transitions

When an electron transitions from a higher energy level to a lower one, the energy difference is emitted as a photon. The exact wavelength of this photon is determined by the energy difference between the two levels, which for hydrogen?like ions depends on both the principal quantum numbers and the square of the nuclear charge.

Inverse Wavelength and Emission

The wavelength of the emitted radiation is inversely related to the transition energy (or wavenumber). The Rydberg formula provides the reciprocal wavelength, meaning that higher energy differences produce larger wavenumbers and consequently shorter wavelengths of emitted radiation.

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