What is the de Broglie wavelength formula?

The de Broglie wavelength of any particle is λ = h/p, where h is Planck's constant (6.626 × 10⁻³⁴ J·s) and p is the particle's momentum (mass × velocity). Heavier or faster particles have shorter wavelengths. For an electron, the wavelength is around an atomic diameter.

What is the de Broglie wavelength of an electron accelerated through V volts?

For an electron accelerated through V volts, the NEET shortcut formula is λ ≈ √(150/V) Å. At V = 150 volts, λ comes out to exactly 1 Å. At V = 100 volts, λ ≈ 1.23 Å. Memorize the shortcut — it appears in NEET almost every year.

Why don't we see the wave nature of a cricket ball?

A cricket ball's mass is so large that its de Broglie wavelength is around 10⁻³⁴ metres — many orders of magnitude smaller than any atom. No instrument can detect wavelengths that small, so the wave behaviour stays hidden. Wave nature only becomes observable for very light particles like electrons.

What did the Davisson-Germer experiment prove?

In 1927, Davisson and Germer fired electrons at a nickel crystal and observed a diffraction peak at φ = 50° when V = 54 V. Diffraction is a wave phenomenon, so this was the first direct experimental proof that electrons behave as waves, confirming de Broglie's 1924 hypothesis.

How does de Broglie's wave hypothesis explain Bohr's quantization?

Bohr's quantization condition mvr = nh/2π can be rewritten as nλ = 2πr using λ = h/mv. This means an electron's orbit is allowed only when a whole number of de Broglie wavelengths fits around it. Quantized orbits are simply standing waves on a circle.

Is de Broglie wavelength a NEET topic?

Yes, the de Broglie hypothesis is part of the Dual Nature of Radiation and Matter chapter and appears in NEET regularly. Common question types include calculating λ for an electron at a given voltage, comparing wavelengths of different particles, and linking λ to Bohr's orbit condition.

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Matter Waves — de Broglie, Davisson-Germer & Quantization

Dual Nature of Radiation and Matter

Explore the interactive model.

pick a particle · watch λ shift 30 orders of magnitude · try V = 54 V on the Davisson-Germer panel

How to use this lab

1Koi particle pick karo (electron se cricket ball tak).
2Dekho de Broglie λ kaise ~30 orders of magnitude badalti hai.
3Davisson-Germer panel pe V = 54 V try karo.

About this lab

Every particle is also a wave. Drag a slider to watch a cricket ball's wavelength shrink to nothing, then see why an electron in an atom has no choice but to form a standing wave. Includes a NEET formula decoder and the historic 1927 Davisson-Germer experiment.

What you're seeing

Har cheez ek wave hai — cricket ball, bullet, electron. de Broglie (1924) ne propose kiya ki har particle ki ek wavelength hoti hai: λ = h/p. Heavy objects ki wavelength itni chhoti hoti hai ki measure karna impossible hai. Electron ki wavelength ek atom ke barabar hoti hai — isi liye electrons atoms mein standing waves form karte hain. Yahi hain orbitals.

Key NEET facts

de Broglie equation: λ = h/p = h/(mv)
every particle has a wavelength — heavy = hidden, light = longer
Electron through V volts: λ ≈ √(150/V) Å
the NEET shortcut — at V = 150 volts, λ = 1 Å exactly
Davisson-Germer (1927): Peak at φ = 50° when V = 54 V
first experimental proof that electrons diffract like X-rays
Bohr's quantization explained: nλ = 2πr ⇒ mvr = nh/2π
n full wavelengths must fit around the orbit — that's why orbits are quantized

Memory trick

λ = h/p — Heavy mass = Hidden wavelength. Lighter mass = Longer wavelength.

Practice

Test Yourself

An electron is accelerated through a potential difference of 100 V. Its de Broglie wavelength is closest to:

Next lab

Matter Waves 3D — Standing Waves Around the Nucleus

Dual Nature of Radiation and Matter

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