Step 1: Understanding the de Broglie Hypothesis.
In 1924, Louis de Broglie proposed that all matter exhibits wave-like properties. He suggested that a particle with momentum (p) has an associated wavelength (
). This is known as the wave-particle duality of matter.
Step 2: The de Broglie Equation.
The equation that relates the wavelength (
) of a particle to its momentum (p) is:
Where:
- is the de Broglie wavelength.
- h is Planck's constant (6.626 10 J·s).
- p is the momentum of the particle.
Step 3: Expressing Momentum.
Momentum (p) of a particle is defined as the product of its mass (m) and its velocity (v):
Step 4: Substituting Momentum in the de Broglie Equation.
By substituting the expression for momentum into the de Broglie equation, we get the most common form of the equation:
Step 5: Evaluating the Options.
- (A) : Incorrect.
- (B) : Correct. This is the de Broglie equation.
- (C) : Incorrect. This would imply .
- (D) : Incorrect. It uses a different symbol ( ) instead of Planck's constant (h).
Step 6: Final Answer.
The correct representation of the de Broglie equation is
.