The wavelength of $L_{\alpha}$ line in $X$-ray spectrum of $_{78}Pt$ is $1.32 \ \mathring{A}$. The wavelength of $L_{\alpha}$ line in $X$-ray spectrum of another unknown element is $4.17 \ \mathring{A}$. If the screening constant for the $L_{\alpha}$ line is $7.4$,then the atomic number of the unknown element is:

In an $X$-ray tube, electrons emitted from a filament (cathode) carrying current $I$ hit a target (anode) at a distance $d$ from the cathode. The target is kept at a potential $V$ higher than the cathode, resulting in the emission of continuous and characteristic $X$-rays. If the filament current $I$ is decreased to $I/2$, the potential difference $V$ is increased to $2V$, and the separation distance $d$ is reduced to $d/2$, then:
$(A)$ The cut-off wavelength will reduce to half, and the wavelengths of the characteristic $X$-rays will remain the same.
$(B)$ The cut-off wavelength as well as the wavelengths of the characteristic $X$-rays will remain the same.
$(C)$ The cut-off wavelength will reduce to half, and the intensities of all the $X$-rays will decrease.
$(D)$ The cut-off wavelength will become two times larger, and the intensity of all the $X$-rays will decrease.

The energy of the $K_\alpha$ $X$-ray line of an element is $8578$ units,and the energy of the $L$ level is $-2859$ units. The energy of the $K$ level is . . . . . . units.

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

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 $0.25 \, \mathring{A}$.

The wavelength of $X-$rays is