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: State the de Broglie idea.
De Broglie said that every moving particle behaves like a wave. The wavelength of this matter wave links to its momentum.

Step 2: Write the basic relation.
The de Broglie wavelength is \[ \lambda = \frac{h}{p} \] where $h$ is Planck's constant and $p$ is the momentum.

Step 3: Write the momentum.
Momentum is mass times velocity. \[ p = mv \]

Step 4: Substitute the momentum.
Put $p = mv$ into the wavelength formula. \[ \lambda = \frac{h}{mv} \]

Step 5: Read the meaning.
A heavier or faster particle has a smaller wavelength. That is why big objects do not show wave behavior in daily life.

Step 6: State the answer.
The de Broglie wavelength is Planck's constant divided by mass times velocity. \[ \boxed{\lambda = \frac{h}{mv}} \]