Calculate the wavelength of the $K_{\alpha}$ line for $Z=31$, when $a=5 \times 10^7 \, Hz^{1/2}$ for a characteristic $X$-ray spectrum.

The wavelength of the $K\alpha$ line in copper is $1.54 \ \mathring{A}$. The ionization energy of the $K$ electron in copper in Joules is:

$(a)$ An $X$-ray tube produces a continuous spectrum of radiation with its short wavelength end at $0.45\,\mathring{A}$. What is the maximum energy of a photon in the radiation?
$(b)$ From your answer to $(a)$,guess what order of accelerating voltage (for electrons) is required in such a tube?

The minimum wavelength of $X$-rays produced in a Coolidge tube operating at $40 \ kV$ is ..... $\mathring A$.

The wavelength of an $X$-ray beam is $10 \, \mathring{A}$. The mass of a fictitious particle having the same energy as that of the $X$-ray photons is $\frac{x}{3} h \, \text{kg}$. The value of $x$ is ....... . ($h =$ Planck's constant)

Find the ratio of the energy of an $X$-ray photon with a wavelength of $1 \mathring A$ to the energy of a visible light photon with a wavelength of $5000 \mathring A$.