MATTER WAVES

de Broglie · Standing Waves · Orbitals

Har cheez ek wave hai. Cricket ball, bullet, electron — sab. Lekin sirf chhoti cheezon ki wave dikhti hai, kyunki badi cheezon ki wavelength itni microscopic hoti hai ki measure karna impossible hai.

Electron ki wavelength ek atom ke barabar hoti hai. Isi liye electrons atoms mein standing waves banate hain — jise hum orbitals kehte hain.

PANEL 01 · HERO

FIT THE WAVE

An electron's wave must close on itself around the nucleus. Only whole numbers of wavelengths are allowed. This is why orbits are quantized.

Wavelengths around orbit (n) 2.00

ALLOWED · n = 2 Standing wave closes on itself — this is Bohr's quantization.

Drag the slider to any integer (1, 2, 3 …): the wave closes and glows green. Drag to a fraction (1.5, 2.7 …): the wave's ends don't meet, destructive interference cancels it, orbit forbidden.

PANEL 02 · CALCULATOR

FIND λ

Every NEET de Broglie MCQ uses one form of λ = h/p. Pick the particle and what's given.

Particle

What's given?

m/s

de Broglie λ

—

Enter a value above

Try this: pick "Cricket ball" with velocity 30, then "Electron" with velocity 1e6. Watch λ jump 24 orders of magnitude. That is why heavy things never diffract.

PANEL 03 · NEET TOOLBOX

REMEMBER THESE

Master formula

λ = h/p = h/(mv)

h = 6.626 × 10⁻³⁴ J·s · works for every particle

Electron shortcut

λ ≈ √(150/V) Å

V in volts · works only for electrons

Bohr quantization

mvr = nh/2π

because n full λ must fit: nλ = 2πr

Memory trick

Heavy = Hidden

large mass → tiny wavelength → never observed