The 1913 law relating X-ray-line frequency to atomic number is Moseley’s law.
English physicist Henry Moseley developed the relationship while measuring characteristic X-rays emitted by different elements. He found that the square root of an X-ray’s frequency increases approximately in proportion to the element’s atomic number, commonly written as ν = A(Z − b)², with constants varying by spectral series.
The discovery gave atomic number a physical meaning. Before Moseley’s work, it was largely an ordering label in the periodic table, and atomic mass created confusing cases such as cobalt and nickel. X-ray measurements showed that cobalt is element 27 and nickel is element 28, supporting their chemical order.
A common mix-up is to describe Moseley’s law as a wavelength law. The measurements involved wavelengths, but the law is usually stated in terms of frequency; because frequency and wavelength are inversely related, either form can describe the same X-ray data. Moseley’s results also helped identify gaps for undiscovered elements.