A proton and an electron are accelerated by the same potential di…

Question

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.

$\lambda_\text{e}=\lambda_\text{p}.$
$\lambda_\text{e}<\lambda_\text{p}.$
$\lambda _\text{e}>\lambda_\text{p}.$
The relation between $\lambda_\text{e}$, and $\lambda_\text{p}$ depends on the accelerating potential difference.

✓

Answer

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

Explanation:

Let m_e and m_p 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

Explore more

More "M.C.Q (1 Marks)" from Photoelectric Effect and WaveParticle Duality→Photoelectric Effect and WaveParticle Duality — all question types→Physics STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Calculate the de-Brogile wavelength of an electron travelling at 1% of the speed of light:

→

The force acting between proton and proton inside the nucleus is

(a) Coulombic

(b) Nuclear

(d) None of these

→

In a region of constant potential:

→

Peltier coefficient for the junction of a pair of metals is proportional to

(a) T absolute temperature of the junction

(b) Square of absolute temperature of the junction

(c)

(d)

→

In non-resonant circuit, what will be the nature of the circuit for frequencies higher than the resonant frequency?

→

If 64 charged drops of water are mixed to form one big drop, then how many times the value of potential on the big drop will be from the full value?

→

and represent mass of neutron and proton respectively. If an element having atomic mass M has N-neutron and Z-proton, then the correct relation will be