Question

The wavelength of de Broglie wave associated with any moving particle does not depend on

• A. mass
• B. charge
• C. velocity
• D. momentum

Hint:

de Broglie wavelength depends on the momentum of the particle, which is a product of its mass and velocity, but not on its charge.

Answer 1

The Correct Option is B

Step 1: de Broglie wavelength.
According to de Broglie’s hypothesis, every moving particle has a wave associated with it. The wavelength \( \lambda \) of the de Broglie wave is given by: \[ \lambda = \frac{h}{p} \] where \( h \) is Planck's constant and \( p \) is the momentum of the particle.
Step 2: Dependence of wavelength.
The momentum \( p \) is related to the mass \( m \) and velocity \( v \) of the particle: \[ p = mv \] Thus, the de Broglie wavelength depends on the mass and velocity of the particle, but not on its charge.
Step 3: Elimination.
- (A) mass: The wavelength depends on mass, as momentum depends on mass.
- (B) charge: Correct, charge does not affect the de Broglie wavelength.
- (C) velocity: The wavelength depends on velocity, as momentum is velocity-dependent.
- (D) momentum: The wavelength depends on momentum, as per de Broglie's relation.
Step 4: Conclusion.
Thus, the de Broglie wavelength does not depend on the charge of the particle.