Example 3 Find the wavelength emitted by a helium ion He^+ during the transition of electron from the second energy level to the first (um)

To determine the wavelength emitted by a helium ion ( ) during the transition of an electron from the second energy level to the first, we can use the Rydberg formula for hydrogen-like atoms: where:- is the wavelength of the emitted photon,- is the Rydberg constant ( ),- and are the principal quantum numbers of the lower and higher energy levels, respectively.For the transition from the second energy level ( ) to the first energy level ( ) in a helium ion ( ), the formula becomes: Now, substituting the value of the Rydberg constant: Therefore, the wavelength emitted by a helium ion ( ) during the transition of an electron from the second energy level to the first is approximately 102.2 nanometers (nm).