The potential difference applied to an $X$-ray tube is increased. As a result,in the emitted radiation

When an $X$-ray of wavelength $0.5 \, \mathring{A}$ passes through a metal foil of thickness $3.5 \, mm$,its intensity is reduced to one-fourth of its initial value. The absorption coefficient of the metal is ..... $mm^{-1}$.

Penetrating power of $X-$rays can be increased by

The order of voltage applied across the ends of an $X$-ray tube is ...... $V$.

$\Delta \lambda$ 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:

An $X$-ray machine has an accelerating potential difference of $25,000$ volts. By calculation, the shortest wavelength will be obtained as....... $\mathring{A}$ ($h = 6.62 \times 10^{-34} \text{ J-s}$; $e = 1.6 \times 10^{-19} \text{ C}$).