Question

What is the de Broglie wavelength of a particle at rest?

• A. Zero
• B. Infinite
• C. One
• D. Undefined

Hint:

The de Broglie wavelength is inversely proportional to momentum. Lower momentum means larger wavelength; if momentum approaches zero, wavelength becomes extremely large.

Answer 1

The Correct Option is B

Concept: According to de Broglie hypothesis, every moving particle has an associated wavelength given by \[ \lambda = \frac{h}{p} \] where \(\lambda\) = de Broglie wavelength, \(h\) = Planck's constant, \(p\) = momentum of the particle.

Step 1: Express momentum. Momentum of a particle is \[ p = mv \] where \(m\) is mass and \(v\) is velocity.

Step 2: Consider a particle at rest. For a particle at rest, \[ v = 0 \] \[ p = 0 \]

Step 3: Substitute into de Broglie equation. \[ \lambda = \frac{h}{0} \] Thus, \[ \lambda = \infty \] Hence, the wavelength of a particle at rest is infinite.