Chapter 15 De Broglie

Question 1

What problem in Bohr’s model did de Broglie help solve?

Answer 1

He explained why electrons in atoms occupy discrete orbits by proposing they behave as standing waves that fit around the nucleus.

Question 2

What is the de Broglie wavelength equation?

Answer 2

λ = h/p = h/mv,
where λ = wavelength, h = Planck’s constant, m = mass, v = velocity.

Question 3

Worked Example – An electron with v = 4.0 × 10^6 m/s.
Calculate its wavelength (mass of e⁻ = 9.11 × 10^-31 kg).

Answer 3

λ = 6.63×10^-34 / (9.11×10^-31 × 4.0×10^6)
≈ 1.8 × 10^-10 m = 0.18 nm.

Question 4

Why don’t we observe wave properties for everyday objects (like a cricket ball)?

Answer 4

Their de Broglie wavelength is extremely small (~10^-35 m), too tiny to produce measurable diffraction or interference effects.

Question 5

What evidence confirmed de Broglie’s hypothesis?

Answer 5

The Davisson–Germer and G.P. Thomson experiments showed diffraction patterns when beams of electrons passed through crystals.

Question 6

What practical technology relies on the wave nature of electrons?

Answer 6

The electron microscope, which achieves higher resolution than optical microscopes because electron wavelengths are shorter than visible light.

Question 7

What is wave–particle duality?

Answer 7

The concept that light and matter exhibit both wave-like and particle-like behaviour, depending on the experiment.

Question 8

What is Heisenberg’s uncertainty principle?

Answer 8

It is impossible to know both the
-** position (Δx) and
-momentum (Δp) **
of a particle with absolute precision. Δx Δp ≳ h/4π.

Question 9

Why is uncertainty negligible for everyday objects but significant at atomic scales?

Answer 9

Because h is so small that uncertainties are only noticeable for very small masses and dimensions (like electrons).

Question 10

What is Schrödinger’s contribution to atomic theory?

Answer 10

He developed a** wave equation** (Ψ) describing the probability distribution of electrons. This led to the concept of orbitals instead of fixed orbits.

you do not need to remember the actual equation

Question 11

What limitations remained in de Broglie’s model?

Answer 11

It explained quantised orbits but not:
1. Multi-electron atoms,
2. Fine structure of spectra,
3. Electron probability distributions (which Schrödinger later explained).