JEE Main 2023 — Structure Of Atom Question with Solution

The number of true statements about the emitted radiation is 2, i.e. statements (A) and (C).

(A) is True: The de-Broglie wavelength of an electron can be calculated as lambda = h / p, where h is Planck's constant and p is the momentum of the electron. The momentum of an electron with a velocity of 1000 m/s is mv, where m is the mass of an electron. Plugging in the values, we get

$\begin{array}{rl}& {\mathrm{V}}_{\mathrm{e}}=1000\mathrm{m}/\mathrm{s};\mathrm{h}=6\times 10^{-34}\mathrm{Js}\\ & \\ & {\mathrm{m}}_{\mathrm{e}}=9\times 10^{-31}\mathrm{kg}\\ & \\ & \lambda =\frac{\mathrm{h}}{\mathrm{mv}}=\frac{6\times 10^{-34}}{9\times 10^{-31}\times 1000}=666.67\times 10^{-9}\mathrm{m}\\ & \\ & =666.67\mathrm{nm}\end{array}$,

(B) is False : The characteristic of electrons emitted is independent of the material of the electrodes of the cathode ray tube.

(C) is True: In a cathode ray tube, electrons are emitted from the cathode and move towards the anode under the influence of an electric field.

(D) is False: The nature of the emitted electrons does not depend on the nature of the gas present in the cathode ray tube, but rather on the material of the electrodes and the potential difference applied across them.