Question

The de Broglie wave corresponding to a particle of mass m and velocity v has a wavelength associated with it

• A. $\frac{h}{mv}$
• B. $hmv$
• C. $\frac{mh}{v}$
• D. $\frac{m}{hv}$

Answer 1

The Correct Option is A

To determine the wavelength associated with a particle, we use the concept of de Broglie wavelength. According to de Broglie, particles such as electrons have wave-like properties, and their wavelength can be calculated using the following formula:

\lambda = \frac{h}{p}

where:

• \lambda is the de Broglie wavelength.
• h is Planck's constant, approximately 6.626 \times 10^{-34} Js.
• p is the momentum of the particle, which is the product of mass m and velocity v of the particle.

Therefore, the momentum p can be expressed as:

p = mv

Substituting the expression for momentum into the de Broglie equation gives:

\lambda = \frac{h}{mv}

Thus, the wavelength associated with a particle of mass m moving with velocity v is given by \frac{h}{mv}, making this the correct answer.

Explanation of Options:

• \frac{h}{mv}: Correct - This is the de Broglie wavelength formula.
• hmv: Incorrect - It suggests the product of Planck's constant, mass, and velocity, which is unrelated to the wavelength.
• \frac{mh}{v}: Incorrect - This reverses the roles of mass and velocity in the formula.
• \frac{m}{hv}: Incorrect - This formula inversely relates mass and velocity, which does not apply to the wavelength.

Thus, the correct answer is \frac{h}{mv}.