In producing $X$-rays,a beam of electrons accelerated by a potential difference $V$ is made to strike a metal target. For what value of $V$ will the $X$-rays have the lowest wavelength of $0.3094 \ \mathring{A}$? (in $kV$)

The energy of the $L$ shell is $7200$ units and the energy of the $K$ shell is $1800$ units. Therefore,the energy of the $K_\alpha$ line is equal to ...... units.

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

The ionization energies of Cobalt $(Co)$,Copper $(Cu)$,and Molybdenum $(Mo)$ are $7.8 \, keV$,$9.0 \, keV$,and $20.1 \, keV$ respectively. If any of these metals are used as a target in an $X$-ray tube operating at $15 \, kV$,then:

$X$-rays of wavelength $0.140 \,nm$ are scattered from a block of carbon. What will be the wavelengths of $X$-rays scattered at $90^{\circ}$ (in $\,nm$)?

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 $0.25 \, \mathring{A}$.