$X$-rays of wavelength $\lambda = 1\,\mathring{A}$ have a frequency of:

The wavelength of the ${K_\alpha}$ line for an element of atomic number $29$ is $\lambda$. Then the wavelength of the ${K_\alpha}$ line for an element of atomic number $15$ is (Take Moseley's constant $b = 1$ for both elements).

Two elements $A$ and $B$ with atomic numbers $Z_{A}$ and $Z_{B}$ are used to produce characteristic $X$-rays with frequencies $v_{A}$ and $v_{B}$ respectively. If $Z_{A}: Z_{B} = 1: 2$, then $v_{A}: v_{B}$ will be

For hard $X$-rays,which of the following is true?

$STATEMENT-1$: If the accelerating potential in an $X$-ray tube is increased, the wavelengths of the characteristic $X$-rays do not change. because
$STATEMENT-2$: When an electron beam strikes the target in an $X$-ray tube, part of the kinetic energy is converted into $X$-ray energy.

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 ........... $\mathring{A}$.