An electron beam is accelerated by a potential difference of $V$ and strikes a metal target to produce $X$-rays. For which of the following values of $V$ (in $kV$) will the $X$-ray wavelength be the shortest?

An $X$-ray beam of wavelength $1 \ \mathring A$ is incident on a crystal with a lattice spacing of $2.8 \ \mathring A$. Find the value of the Bragg angle in degrees for the first-order diffraction.

$X$-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 $\,nm$)?

$\Delta \lambda$ is the difference between the wavelength of the $K_\alpha$ line and the minimum wavelength of the continuous $X$-ray spectrum when the $X$-ray tube is operated at a voltage $V$. If the operating voltage is changed to $V / 3$,then the above difference is $\Delta \lambda^{\prime}$. Then:

$20 \ kV$ electrons can produce $X$-rays with a minimum wavelength of

In a Coolidge tube experiment, the minimum wavelength of the continuous $X-$ray spectrum is equal to $66.3\, pm$. Then: