Wave Characteristics

To determine the graph that represents the variation of the de Broglie wavelength (λ) with respect to momentum (p), we need to analyze the relationship between these two quantities. According to the de Broglie hypothesis, the wavelength of a particle is given by:

where:

• λ is the de Broglie wavelength.
• h is the Planck's constant.
• p is the momentum of the particle.

This equation indicates that the de Broglie wavelength is inversely proportional to the momentum. Hence, as momentum increases, the wavelength decreases, and vice versa. Graphically, this inverse relationship is represented by a hyperbolic curve when plotting λ versus p.

Given the options and the inverse relationship, the correct graph will demonstrate a hyperbolic decrease in λ as p increases, consistent with an inverse proportionality relation. Therefore, the correct answer corresponds to the graph with option (D).