The $K_{\alpha}$ $X$-ray emission line of tungsten occurs at $\lambda = 0.021 \ nm$. The energy difference between $K$ and $L$ levels in this atom is about:

The minimum wavelength of $X$-rays produced by $20 \ kV$ electrons is nearly (in $Å$)

Bragg's law for $X$-rays is

The maximum distance between the inter-atomic planes of a crystal is $10^{-7} \ cm$. The maximum wavelength of $X$-rays that can be studied by this crystal is ........... $\mathring{A}$.

An $X$-ray tube produces a continuous spectrum of radiation with its shortest wavelength of $45 \times 10^{-2} \text{ Å}$. The maximum energy of a photon in the radiation in $eV$ is (in $27,500$). $(h = 6.62 \times 10^{-34} \text{ J-s}, c = 3 \times 10^8 \text{ m/s})$.

An $X$-ray tube operates at $50 \, kV$ and $20 \, mA$. The target material has a mass of $1.0 \, kg$ and a specific heat capacity of $495 \, J \cdot kg^{-1} \cdot ^\circ C^{-1}$. One percent of the applied electrical power is converted into $X$-rays,and the remaining energy is used to heat the target. Then:
$(1)$ $A$ suitable target material should have a high melting point.
$(2)$ $A$ suitable target material should have low thermal conductivity.
$(3)$ The rate of rise of temperature of the target is $2 \, ^\circ C/s$.
$(4)$ The minimum wavelength of the emitted $X$-rays is $0.25 \, \mathring{A}$.