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: Write the de-Broglie relation.
The wavelength associated with a moving particle is
\[ \lambda = \frac{h}{p} = \frac{h}{mv}, \]
where \( h \) is Planck's constant, \( p \) the momentum, \( m \) the mass and \( v \) the velocity.

Step 2: Read off the dependences.
The formula contains momentum \( p \) (option iv), and through \( p = mv \) it also depends on mass \( m \) (option i) and velocity \( v \) (option ii).

Step 3: Look for what is missing.
Nowhere in \( \lambda = h/mv \) does the charge \( q \) of the particle appear. The de-Broglie wavelength is a purely mechanical quantity, set only by momentum. So it does not depend on charge.

Step 4: Conclusion.
Option (iii), charge, is the correct choice.

\[\boxed{\lambda = \frac{h}{mv}\ \text{is independent of charge}}\]