How does the wavelength $\lambda$ of the $K_\alpha$ line in the $X$-ray spectrum depend on the atomic number $Z$?

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:

$X$-rays of wavelength $0.1 \ \mathring A$ are allowed to fall on a metal and get scattered. The wavelength of the scattered radiation is $0.111 \ \mathring A$. If $h = 6.624 \times 10^{-34} \ J \cdot s$ and $m_0 = 9 \times 10^{-31} \ kg$,then the direction of the scattered photons will be:

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

Moseley's law for characteristic $X$-rays is given by $\sqrt{f} = a(Z - b)$. Choose the correct statement.

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 $0.25 \, \mathring{A}$.