Moseley studied the $X$-ray spectra of various elements. The spectral line observed were of
(i) short wavelength $-K$ series and
(ii) long wavelength $-L$ series. $K_{\alpha}$ line is most intense in the $K$-series. Moreover, he observed that the wavelength of the $K_{\alpha}$ line decreases with increase in the atomic number of the element as the target. If a graph is plotted between the square root of the frequency and the atomic number of the element emitting the line, it is a straight line Thus, $\sqrt{f} \propto Z$
Where $\sqrt{f}$ is the frequency of the radiation and $Z$ is the atomic number of the element.
The emission spectrum of a chemical element or chemical compound is the spectrum of frequencies of electromagnetic radiation emitted due to an electron making a transition from a high energy state to a lower energy state. The photon energy of the emitted photon is equal to the energy difference between the two states.
Read More: Atomic Spectra
The Rydberg formula is the mathematical formula to compute the wavelength of light.
\[\frac{1}{\lambda} = RZ^2(\frac{1}{n_1^2}-\frac{1}{n_2^2})\]Where,
R is the Rydberg constant (1.09737*107 m-1)
Z is the atomic number
n is the upper energy level
n’ is the lower energy level
λ is the wavelength of light
Spectral series of single-electron atoms like hydrogen have Z = 1.