Introduction to Quantum Physics
Step into the strange world of quantum mechanics -- where light behaves as both a wave and a particle, and energy comes in discrete packets called quanta.
The Photoelectric Effect
The photoelectric effect is the emission of electrons from a metal surface when light of sufficient frequency shines upon it. Classical wave theory could not explain this phenomenon -- it was Einstein's explanation using photons (light quanta) in 1905 that earned him the Nobel Prize.
How the Photoelectric Effect Works
Photon
Energy = hf
Metal Surface
Work function = φ
Electron Ejected
KEmax = hf - φ
Einstein's photoelectric equation: KEmax = hf - φ, where h is Planck's constant (6.63 × 10-34 J·s), f is the frequency of light, and φ is the work function of the metal.
Classical Predictions (Wrong)
- • Brighter light = more KE (wrong)
- • Any frequency should work (wrong)
- • Time delay before emission (wrong)
Quantum Explanation (Correct)
- • Higher frequency = more KE
- • Threshold frequency f0 required
- • Instantaneous emission
Wave-Particle Duality
One of the most profound ideas in quantum physics is that all matter and radiation exhibit both wave-like and particle-like behaviour. This was first proposed for light and later extended to all matter by Louis de Broglie in 1924.
Wave Evidence
Diffraction: Light bends around obstacles and through slits, producing interference patterns.
Young's double-slit experiment: Light passing through two slits creates an interference pattern of bright and dark fringes.
This can only be explained by wave behaviour.
Particle Evidence
Photoelectric effect: Light ejects electrons one at a time, with energy dependent on frequency, not intensity.
Compton scattering: X-rays scatter off electrons like billiard balls, with momentum transfer.
This can only be explained by particle behaviour.
De Broglie Wavelength
λ = h / p = h / (mv)
Every particle with momentum p has an associated wavelength λ. For everyday objects, λ is incredibly tiny and undetectable. For electrons, λ is comparable to atomic spacings.
Electron diffraction: When electrons are fired at a thin crystal, they produce a diffraction pattern just like X-rays -- confirming that particles have wave properties. This was demonstrated by Davisson and Germer in 1927.
Photon Energy and Atomic Spectra
Light is quantised into photons, each carrying a discrete amount of energy. When atoms absorb or emit photons, electrons jump between specific energy levels, producing characteristic line spectra.
Photon Energy Equations
E = hf
Energy from frequency
E = hc / λ
Energy from wavelength
Energy Level Transitions
Hydrogen atom energy levels (not to scale)
Key relationship: When an electron drops from a higher level (Ei) to a lower level (Ef), a photon is emitted with energy Ephoton = Ei - Ef = hf. This explains why each element has a unique emission spectrum.
Key Vocabulary
Photon
A quantum (discrete packet) of electromagnetic radiation with energy E = hf. Photons have zero rest mass and always travel at the speed of light.
Work Function (φ)
The minimum energy required to liberate an electron from the surface of a metal. Different metals have different work functions.
Threshold Frequency (f0)
The minimum frequency of light needed to eject electrons from a metal surface. Below this frequency, no electrons are emitted regardless of intensity.
De Broglie Wavelength
The wavelength associated with a moving particle, given by λ = h/p. Demonstrates that matter has wave-like properties.
Worked Examples
Calculate the energy of a photon of ultraviolet light with frequency 1.5 × 1015 Hz.
Step 1: Use E = hf, where h = 6.63 × 10-34 J·s.
Step 2: E = 6.63 × 10-34 × 1.5 × 1015.
Step 3: E = 9.945 × 10-19 J ≈ 9.95 × 10-19 J.
Answer: The photon energy is approximately 9.95 × 10-19 J (or about 6.2 eV).
Light of frequency 8.0 × 1014 Hz strikes a metal with work function 3.0 × 10-19 J. Find the maximum kinetic energy of the emitted electrons.
Step 1: Find photon energy: E = hf = 6.63 × 10-34 × 8.0 × 1014 = 5.304 × 10-19 J.
Step 2: Apply Einstein's equation: KEmax = hf - φ.
Step 3: KEmax = 5.304 × 10-19 - 3.0 × 10-19 = 2.3 × 10-19 J.
Answer: The maximum KE of emitted electrons is 2.3 × 10-19 J (about 1.4 eV).
Calculate the de Broglie wavelength of an electron (mass 9.11 × 10-31 kg) moving at 2.0 × 106 m/s.
Step 1: Calculate momentum: p = mv = 9.11 × 10-31 × 2.0 × 106 = 1.822 × 10-24 kg·m/s.
Step 2: Apply de Broglie: λ = h/p = 6.63 × 10-34 / 1.822 × 10-24.
Step 3: λ = 3.64 × 10-10 m = 0.364 nm.
Answer: The de Broglie wavelength is 3.64 × 10-10 m -- comparable to atomic spacing, so electron diffraction is observable.
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
In the photoelectric effect, increasing the intensity of light above the threshold frequency will:
Question 2
The de Broglie wavelength of a particle will decrease if:
Question 3
A photon has a wavelength of 500 nm. Its energy is closest to:
Question 4
Which experiment provided the first direct evidence for the particle nature of light?
Question 5
If the frequency of incident light on a metal surface is doubled (while remaining above the threshold), the maximum kinetic energy of emitted electrons:
Key Concepts Summary
- ●The photoelectric effect shows light behaves as particles (photons): KEmax = hf - φ.
- ●Wave-particle duality: All matter and radiation exhibit both wave and particle properties.
- ●The de Broglie wavelength λ = h/p relates a particle's momentum to its wave-like properties.
- ●Photon energy is quantised: E = hf = hc/λ. Higher frequency means higher energy.
- ●Atomic emission spectra result from electrons transitioning between discrete energy levels.