Question 24: The minimum wavelength of X-rays produced by an electron accelerated through a potential difference of V volts is proportional to:
(1) \frac{1}{\sqrt{V}}
(2) V^{2}
(3) \sqrt{V}
(4) \frac{1}{V}
Answer: Option (4)
Explanation:
When electrons are accelerated through a potential difference V,
they gain kinetic energy equal to
E = eVIn an X-ray tube, the minimum wavelength of X-rays is produced when
the entire kinetic energy of the electron is converted into a single photon.
Energy of a photon is given by
E = \frac{hc}{\lambda_{\min}}Equating the two energies,
eV = \frac{hc}{\lambda_{\min}}Rearranging,
\lambda_{\min} = \frac{hc}{eV}Thus, the minimum wavelength is inversely proportional to the accelerating voltage.
\lambda_{\min} \propto \frac{1}{V}Therefore, the correct answer is Option (4).