Question

The wavelength of the de-Broglie wave associated with a moving particle does not depend on:

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

Hint:

Recall \( \lambda = h/mv \). Which of mass, velocity, momentum or charge is absent from this formula?

Answer 1

The Correct Option is C

Step 1: Start from momentum, not charge.
Louis de Broglie linked a particle's wavelength only to its momentum: \(\lambda = h/p\). Momentum for a slow particle is \(p = mv\), so the wavelength is fully determined once mass and speed are known.

Step 2: Expand the variables inside the formula.
Substituting \(p = mv\) gives \(\lambda = h/(mv)\). This single expression already involves momentum, mass and velocity, so options (i), (ii) and (iv) all influence \(\lambda\).

Step 3: Note the absent quantity.
Electric charge does not appear anywhere in \(h/(mv)\). Charge affects how a particle responds to electric and magnetic fields, but not the matter-wave wavelength itself for a given momentum.

Step 4: Answer.
Therefore the de-Broglie wavelength does not depend on charge, option (iii).

\[\boxed{\lambda\ \text{independent of charge}}\]