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 pertains to de Broglie's hypothesis, which posits the wave-particle duality of matter.
1. de Broglie Wavelength Formula: * De Broglie proposed that all moving particles, including electrons, exhibit wave-like properties. The de Broglie wavelength \( \lambda \) is defined by the formula: \[ \lambda = \frac{h}{mv} \] * In this formula: * \( h \) represents Planck's constant. * \( m \) denotes the mass of the particle (specifically, an electron in this context). * \( v \) signifies the velocity of the particle. 2. Interpretation of the Formula: * This equation establishes an inverse relationship between a particle's wavelength and its momentum (\( m \times v \)). * An increase in velocity leads to a decrease in wavelength. 3. Evaluation of Options: * Option (1) accurately represents the de Broglie wavelength formula. * Option (2) (\( \lambda = \frac{h}{2mv} \)) is incorrect due to the inclusion of an extraneous factor of 2. * Option (3) (\( \lambda = \frac{mv}{h} \)) is incorrect as it inverts the established relationship. * Option (4) (\( \lambda = \frac{2mv}{h} \)) is incorrect for the same reason as Option (3).