Electrons of mass $m$ with de-Broglie wavelength $\lambda$ fall on the target in an $X$-ray tube. The cutoff wavelength $(\lambda_0)$ of the emitted $X$-ray is

The filament current in the electron gun of a Coolidge tube is increased while the potential difference used to accelerate the electrons is decreased. As a result, in the emitted radiation

If a voltage applied to an $X$-ray tube is increased to $1.5$ times, the minimum wavelength $(\lambda_{\min})$ of an $X$-ray continuous spectrum shifts by $\Delta \lambda = 26 \, pm$. The initial voltage applied to the tube is:

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 ${K_{\alpha }}$ $X$-rays produced by an $X$-ray tube is $0.76 \, \mathring{A}$. The atomic number of the anticathode material is:

The primary difference between $X$-rays and $\gamma$-rays is that: