2023 Dual Nature of Radiation and MatterCut-off Wavelength of X-rays Medium Question 12 of 82 in Dual Nature of Radiation and Matter

The minimum wavelength of X-rays produced by an electron accelerated through a potential difference of $V$ volts is proportional to:

A $V^2$
B $\sqrt{V}$
C $\frac{1}{V}$
D $\frac{1}{\sqrt{V}}$

The answer is C.

Solution

$eV=\frac{hc}{\lambda_{min}}$, so $\lambda_{min}\propto\frac{1}{V}$.

$eV$ = energy of electron; for minimum wavelength, maximum loss of energy: $eV=\left(\frac{hc}{\lambda}\right)$ $\lambda\propto\left(\frac{1}{V}\right)$

Concept λ_min ∝ 1/V

Dual Nature of Radiation and Matter in past papers

82 questions from this chapter have appeared across 27 exam years.