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).

$\Delta \lambda$ 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:

Electrons of mass $m$ with de-Broglie wavelength $\lambda$ fall on a target. The cut-off wavelength $\lambda_0$ is equal to [$h=$ Planck's constant,$c=$ velocity of light].

The $K_{\alpha}$ wavelength emitted by an atom of atomic number $Z = 11$ is $\lambda$. Find the atomic number for an atom that emits $K_{\alpha}$ radiation with wavelength $4\lambda$.

$A$ charged gold leaf electroscope has its leaves apart by a certain amount with enclosed air. When the electroscope is subjected to $X$-rays,then the leaves

Which of the following wavelengths in $\mathring{A}$ represents 'hard' $X$-rays?