MCQ
A proton and an electron are accelerated by the same potential difference. Let $\lambda_\text{e}$ and $\lambda_\text{p}$ denote the de Broglie wavelengths of the electron and the proton respectively.
  • A
    $\lambda_\text{e}=\lambda_\text{p}.$
  • B
    $\lambda_\text{e}<\lambda_\text{p}.$
  • C
    $\lambda _\text{e}>\lambda_\text{p}.$
  • D
    The relation between $\lambda_\text{e}$, and $\lambda_\text{p}$ depends on the accelerating potential difference.

Answer

  1. $\lambda _\text{e}>\lambda_\text{p}.$

Explanation:

Let me and mp be the masses of electron and proton, respectively.

Let the applied potential difference be V.

Thus, the de-Broglie wavelength of the electron,

$\lambda=\frac{\text{h}}{\sqrt{2\text{m}_\text{e}\text{eV}}}\dots(1)$

And de-Broglie wavelength of the proton,

$\lambda=\frac{\text{h}}{\sqrt{2\text{m}_\text{p}\text{eV}}}\dots(2)$

Dividing equation (2) by equation (1), we get:

$\frac{\lambda_\text{p}}{\lambda_\text{e}}=\frac{\sqrt{\text{m}_\text{e}}}{\sqrt{\text{m}_\text{p}}}$

$\text{m}_\text{e}<\text{m}_\text{p}$

$\therefore\frac{\lambda_\text{p}}{\lambda_\text{e}}<1$

$\Rightarrow\lambda_ \text{p}<\lambda_\text{e}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

Assertion  : In high latitude one sees colourful curtains of light hanging down from high altitudes.

Reason      :  The high energy charged particles from the sun are deflected to polar regions by the magnetic field of the earth.

(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.

(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.

(c) If assertion is true but reason is false.

(d) If the assertion and reason both are false.

In order to increase the angular magnification of a simple microscope, one should increase:

Two ions have equal masses but one is singly-ionised and the other is doubly-ionised. They are projected from the same place in a uniform magnetic field with the same velocity perpendicular to the field.
In case of Coulomb’s law, the value of k is given by:

The energy of a charged capacitor is given by the expression (q = charge on the conductor and C = its capacity)

(a)  

(b)

(c) 2qC

(d)

The collector plate in an experiment on photoelectric effect is kept vertically above the emitter plate. Light source is put on and a saturation photocurrent is recorded. An electric field is switched on which has a vertically downward direction.
  1. The photocurrent will increase.
  2. The kinetic energy of the electrons will increase.
  3. The stopping potential will decrease.
  4. The threshold wavelength will increase.
According to Maxwell , most of the optical properties of light depend on:
Which of the following uses the principle of electromagnetic induction?

The impurity atom added to germanium to make it N-type semiconductor is

(a) Arsenic

(b) Iridium

(c) Aluminium

(d) Iodine

Which of the following statement is false: