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Exam level6 past questions

de Broglie Wavelength and Matter Waves

All matter exhibits wave-like properties, with the de Broglie wavelength inversely proportional to momentum and dependent on factors like velocity, temperature, and particle type.

Why this shows up in the exam

NEET tests your ability to calculate de Broglie wavelengths for various particles and conditions, and to understand the implications of matter waves.

How NEET tests this

Application · 3 QsNumerical · 3 QsStatement analysis

Learn the idea

All particles behave like waves; the de Broglie wavelength λ equals Planck’s constant divided by the particle’s momentum, so any change in momentum instantly changes λ – the key insight is λ∝1/p.

🧠 Memory hook: Higher momentum = shorter wavelength – like a fast runner leaves a tiny shadow, a slow walker leaves a long one.

Get this one clearly and it pays off every single time it shows up in the paper. 🎯

Formulas & facts to keep ready

  • λ = h/p (non‑relativistic)
  • p = mv
  • For an electron accelerated through potential V: eV = ½ mv² ⇒ λ = h/√(2meV)
  • For an ideal gas molecule v_rms = √(3kT/m) ⇒ λ ∝ 1/√T
  • In a uniform electric field E, acceleration a = eE/m and v(t)=v₀+at

How to approach it

  1. 1Read the question and decide which relation (λ = h/p, λ = h/√(2meV), or λ ∝ 1/√T) is required
  2. 2Compute the particle’s momentum or speed using the given data (V, T, E, time etc.)
  3. 3Substitute the momentum (or speed) into λ = h/p and simplify
  4. 4Check units and whether any approximation (non‑relativistic) is valid

Worked example — watch it click

An electron of mass m with an initial velocity v = υ₀i(υ₀ > 0) enters in electric field E = E₀i (E₀ = constant > 0). If λ₀ is its de Broglie wavelength initially, then its de Broglie wavelength at time t is:

  • ✅λ₀ / [1 + (eE₀/mv₀)xt]
  • B)λ₀ [1 + (eE₀/mv₀)xt]
  • C)λ₀t
  • D)λ₀

The concept behind this problem

The example asks how λ evolves when the electron’s speed increases linearly under a constant electric field, directly testing λ = h/(mv) and the time‑dependent velocity v(t).

Step by step

  1. 1Initial: λ₀ = h/(mv₀).
  2. 2Under constant electric field E₀, acceleration a = eE₀/m.
  3. 3Velocity at time t: v(t) = v₀ + at = v₀ + (eE₀/m)t = v₀[1 + (eE₀/mv₀)t].
  4. 4Wavelength λ(t) = h/[mv(t)] = h/[mv₀(1 + eE₀t/mv₀)] = λ₀/[1 + (eE₀/mv₀)t].

Watch out

Students often invert the factor and write λ = λ₀[1+(eE₀/mv₀)t] instead of λ = λ₀ divided by that factor.

Common slip-ups that cost marks

  • •Using eV directly without converting to joules (1 eV = 1.602×10⁻¹⁹ J)
  • •Confusing λ ∝ √T with λ ∝ 1/√T for temperature dependence
  • •Applying the relativistic formula when the problem assumes non‑relativistic speeds

🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.

Practise it

These are real questions from past NEET papers that test this exact idea.

Question 1 of 6

An electron is accelerated from rest through a potential difference of V volt. If the de Broglie wavelength of the electron is 1.227 × 10⁻² nm, the potential difference is:

Push further

More challenging

12 harder questions built from the past papers above — a step up in difficulty, with distractors designed so you can't get there by elimination. Written and checked by our reviewers, not from a real paper.

Question 1 of 12

The de Broglie wavelength of a molecule in a gas at temperature T is given by λ. If the temperature of the gas is increased to 4T, what will be the new de Broglie wavelength?

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