Dual Nature of Radiation and Matter
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.
pick a particle · watch λ shift 30 orders of magnitude · try V = 54 V on the Davisson-Germer panel
5 minutes · +4 right, −1 wrong (real NEET marking) · one global leaderboard.
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.
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.
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.
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.
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.
An electron is accelerated through a potential difference of 100 V. Its de Broglie wavelength is closest to: