Question

Calculate the de Broglie wavelength of an electron moving with a given velocity.

• A. \( \lambda = \frac{h}{mv} \)
• B. \( \lambda = \frac{h}{2mv} \)
• C. \( \lambda = \frac{mv}{h} \)
• D. \( \lambda = \frac{2mv}{h} \)

Hint:

To find the wavelength of any particle, use de Broglie's formula \( \lambda = \frac{h}{mv} \). The higher the velocity, the shorter the wavelength!

Answer 1

The Correct Option is A

This question involves de Broglie's hypothesis, which describes the wave-particle duality of matter.
1. de Broglie Wavelength Formula: - According to de Broglie, any moving particle, including electrons, has an associated wave. The de Broglie wavelength \( \lambda \) is given by the formula: \[ \lambda = \frac{h}{mv} \] Where: - \( h \) is Planck's constant, - \( m \) is the mass of the particle (electron in this case), - \( v \) is the velocity of the particle. 2. Understanding the Formula: - This equation tells us that the wavelength associated with a particle is inversely proportional to its momentum (mass \( \times \) velocity). - The higher the velocity, the shorter the wavelength. 3. Analysis of Options: - Option (1) is the correct de Broglie wavelength formula. - Option (2) \( \lambda = \frac{h}{2mv} \) is incorrect because it introduces an unnecessary factor of 2. - Option (3) \( \lambda = \frac{mv}{h} \) is incorrect because it reverses the relationship. - Option (4) \( \lambda = \frac{2mv}{h} \) is incorrect for the same reason as Option (3).