The waves emitted when a metal target is bombarded with high energy electrons are

If $f_1, f_2$,and $f_3$ are the frequencies of $K_\alpha, K_\beta$,and $L_\alpha$ $X$-rays of a given metal,respectively,then:

The difference between $\lambda_{K_{\alpha}}$ and $\lambda_{min}$ becomes twice if the accelerating potential changes from $3100 \ V$ to $12400 \ V$. Find $\lambda_{K_{\alpha}}$ in $\mathring{A}$. (Given $hc = 12400 \ eV \mathring{A}$)

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

$X$-rays are used for the structural analysis of crystals because:

If $10000\, V$ is applied across an $X$-ray tube,what will be the ratio of the de-Broglie wavelength of the incident electrons to the shortest wavelength of $X$-rays produced? (Given: $\frac{e}{m}$ for an electron is $1.8 \times 10^{11}\, C\, kg^{-1}$)