Q.Using Moseley's law in the form $\nu = \dfrac{3}{4}cR(Z-1)^2$ for the $K_\alpha$ line, calculate the wavelength of the $K_\alpha$ X-ray line emitted by a copper target ($Z=29$).

Moseley's Law

Henry Moseley (1913) studied the characteristic X-rays emitted by different metal anodes. He found that the square root of the frequency of a given X-ray line varies linearly with the element's atomic number:

where $a$ and $b$ are constants and $Z$ is the atomic number. Thus a plot of $\sqrt{\nu}$ against $Z$ (not atomic mass) is a straight line.

Moseley's key conclusion was that the atomic number, not the atomic mass, is the fundamental property that orders the elements. This resolved anomalies in Mendeleev's mass-based table (e.g. the Ar/K and Co/Ni pairs), justified the modern periodic law, and predicted gaps for then-undiscovered elements. It also gave physical meaning to $Z$ as the nuclear charge. …