CAPF AC 2020 Q19: Science & Technology – Physics
An electron and a photon have same de Broglie wavelength. It implies that they have the same
- (a) linear momentum
- (b) energy
- (c) speed
- (d) angular momentum
Answer: (a) linear momentum
Explanation
de Broglie wavelength
How to think: write the formula and see which quantity it contains.
de Broglie relation: wavelength = h / p
Here h is Planck's constant and p is linear momentum.
If two particles have the same wavelength, they must have the same momentum.
Nothing else is fixed by the formula.
| Quantity | Electron | Photon | Same? |
|---|---|---|---|
| Linear momentum | h divided by wavelength | h divided by wavelength | Yes |
| Speed | Much less than the speed of light | Speed of light | No |
| Energy | Depends on its mass | Momentum times the speed of light | No |
| Rest mass | Has mass | Zero | No |
Angular momentum does not appear in the relation at all.
Answer: (a) linear momentum.
Why each option is right or wrong
- (a) CORRECT. Wavelength = h / p, so equal wavelengths mean equal linear momentum.
- (b) Incorrect. With equal momentum, the photon and the electron have different energies.
- (c) Incorrect. A photon moves at the speed of light; an electron is always slower.
- (d) Incorrect. Angular momentum is not part of the de Broglie relation.
Key point
de Broglie: wavelength = h / p (Planck's constant divided by linear momentum). Same wavelength means same momentum, not same energy or speed.
Remember
de Broglie wavelength = h / momentum.
Common mistakes
- Choosing energy because both energy and wavelength are linked to Planck's constant.
- Forgetting that the photon has zero rest mass but still has momentum.
- Assuming particles with the same wavelength move at the same speed.
Exam tip
Write the formula first. The answer is the only quantity that appears in it.
Sources
- NCERT Class XII Physics — Dual Nature of Radiation and Matter
- NCERT Class XI Chemistry — Structure of Atom (dual behaviour of matter)