Question

For a matter waves which of the following quantities will be independent of its wavelength?
1. Mass
2. Velocity
3. Momentum
4. Charge

Answer 1

Correct Answer - Option 4 : Charge

CONCEPT:

Dual nature of matter:

• According to de Broglie, the matter has a dual nature of wave-particle.
• The wave associated with each moving particle is called matter waves.
• ​​de Broglie wavelength associated with the particle is given as,

\(⇒ λ = \frac{h}{mv}=\frac{h}{P}\)   

Where, h = Planck's constant, m = mass of a particle, v = velocity of a particle and P = momentum

EXPLANATION:

According to de Broglie, the wavelength of matter waves is given as,

\(⇒ λ = \frac{h}{mv}=\frac{h}{P}\)     -----(1)   

Where, h = Planck's constant, m = mass of a particle, v = velocity of a particle and P = momentum

• By equation 1, it is clear that the wavelength of matter waves depends on the mass, velocity, and momentum of the particle but it is independent of the charge of the particle.
• Hence, option 4 is correct.

Characteristics of Matter waves:

1. ​​The lighter the particle, the greater is the de Broglie wavelength.
2. The higher the velocity of the particle, the smaller is its de Broglie wavelength.
3. The de Broglie wavelength of a particle is independent of the charge or nature of the particle.
4. The matter waves are not electromagnetic in nature. Only charged particles produce electromagnetic waves.