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What does the de Broglie wavelength formula say about an electron’s momentum and wavelength?

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A horizontal gradient bar displays the visible light spectrum from violet to red, labeled with corresponding frequency in terahertz, wavelength in nanometers, and photon energy in electron volts. — light When white light is spread apart by a prism or a diffraction grating, the colours of the visible spectrum appear. The colours vary according to their wavelengths. Violet has the highest frequencies and shortest wavelengths, and red has the lowest frequencies and the longest wavelengths.

The de Broglie wavelength formula describes the wave-particle duality of matter, establishing that particles like electrons exhibit both particle and wave characteristics.12

Proposed by Louis de Broglie in 1924, the relationship states that the wavelength ( $λ$ ) of a moving particle is inversely proportional to its linear momentum ( $p$ ). The formula is expressed as:2

$λ = \frac{h}{p}$

In this equation, $h$ represents Planck’s constant. Because the momentum is in the denominator, the formula indicates that as an electron’s momentum increases, its associated wavelength decreases, and conversely, as its momentum decreases, its wavelength increases. This hypothesis was experimentally confirmed in 1927, demonstrating that electrons behave as waves with a wavelength determined by their momentum.2341