Question

The de Broglie wavelength of a particle of mass $m$ moving with a velocity $v$ is given by

• A. $h / mv$
• B. $mv / h$
• C. $hm / v$
• D. $h / m^2v$

Hint:

Remembering the de Broglie relation and understanding how to manipulate it with basic physics concepts like momentum can help in solving similar problems.

Answer 1

The Correct Option is A

Step 1: Concept
The de Broglie wavelength is a fundamental concept in quantum mechanics, which relates the wavelength $\lambda$ of a particle to its momentum $p$. The relationship was proposed by Louis de Broglie and is given by: \[\lambda = \frac{h}{p}\] where $h$ is Planck's constant and $p$ is the momentum of the particle.

Step 2: Meaning
The wavelength $\lambda$ represents a wave-like property associated with particles, suggesting that all matter exhibits both particle and wave characteristics. The formula shows that the wavelength decreases as the momentum increases.

Step 3: Analysis
Given the de Broglie relation: \[\lambda = \frac{h}{p}\] and knowing that momentum $p$ is defined as: \[p = mv\] where $m$ is the mass of the particle and $v$ is its velocity, we can substitute this into the de Broglie equation to find the wavelength in terms of $m$, $v$, and $h$. Thus, \[\lambda = \frac{h}{mv}\] This matches option A.

Step 4: Conclusion
The correct expression for the de Broglie wavelength is $\lambda = \frac{h}{mv}$, confirming that option A is the right choice. Final Answer: (A)