Optical Phenomena & EM Radiation

Nature of Electromagnetic Radiation

Electromagnetic (EM) radiation consists of oscillating electric and magnetic fields that travel as transverse waves at the speed of light in a vacuum:

c = 3 × 10⁸ m·s⁻¹
E = hf = hc/λ
h = 6.63 × 10⁻³⁴ J·s (Planck's constant)

Symbol	Quantity	Unit
E	Energy of one photon	Joule (J)
h	Planck's constant	J·s
f	Frequency of radiation	Hz (s⁻¹)
λ	Wavelength	metre (m)
c	Speed of light in vacuum	m·s⁻¹

The Electromagnetic Spectrum

All EM waves travel at c but differ in frequency (and wavelength). In order of increasing frequency (decreasing wavelength):

Region	Frequency (Hz)	Wavelength	Key uses
Radio waves	10³–10⁹	km–cm	Broadcasting, communication
Microwaves	10⁹–10¹²	cm–mm	Cooking, radar, mobile phones
Infrared (IR)	10¹²–4×10¹⁴	mm–700 nm	Heat lamps, remote controls, thermal imaging
Visible light	4×10¹⁴–7.5×10¹⁴	700–400 nm	Sight, photography
Ultraviolet (UV)	7.5×10¹⁴–10¹⁷	400–10 nm	Sterilisation, fluorescence, sunburn
X-rays	10¹⁷–10¹⁹	10–0.01 nm	Medical imaging, security scanning
Gamma rays	>10¹⁹	<0.01 nm	Cancer treatment, sterilisation, nuclear medicine

Key rule: Higher frequency → higher photon energy (E = hf) → more penetrating radiation. Gamma rays are the most energetic and penetrating; radio waves the least.

The Photoelectric Effect

When light shines on a metal surface, electrons are ejected — but only if the frequency of light is at or above a minimum threshold frequency f₀. This cannot be explained by wave theory — it requires a particle model.

Einstein's explanation (1905): Light travels in discrete packets called photons, each with energy E = hf. An electron is only ejected if one photon has enough energy to overcome the binding energy of the metal (the work function).

W = hf₀ (work function — minimum energy to eject electron)
hf = W + Ek(max)
Ek(max) = hf − W = hf − hf₀

Frequency below f₀: No electrons ejected, no matter how intense the light
Frequency above f₀: Electrons ejected; increasing f → higher Ek(max)
Increasing intensity (more photons per second): more electrons ejected per second (higher current), but the kinetic energy of each electron does not increase

Evidence for particle nature: The photoelectric effect cannot be explained by waves. Waves would predict that any frequency (given enough time/intensity) could eject electrons. The existence of a sharp threshold frequency proves photons are real quanta of energy.

Emission and Absorption Spectra

Electrons in atoms exist at discrete energy levels. When an electron drops from a higher to a lower energy level, it emits a photon of a specific frequency: E = hf = E₂ − E₁.

Emission spectrum: Hot gas emits light at specific wavelengths → bright coloured lines on a dark background
Absorption spectrum: Cool gas absorbs the same wavelengths from white light passing through → dark lines on a continuous rainbow spectrum
Each element produces a unique spectral pattern → used to identify elements in distant stars (spectroscopy)

Wave-Particle Duality and Lasers

Light behaves as a wave (diffraction, interference) AND as a particle (photoelectric effect, Compton scattering). This is wave-particle duality. de Broglie extended this: all particles (electrons, protons) also have a wavelength:

λ = h / mv (de Broglie wavelength)

Laser = Light Amplification by Stimulated Emission of Radiation. Properties: monochromatic (one wavelength), coherent (all waves in phase), collimated (parallel beam). Uses: surgery, cutting, barcode scanners, fibre optics, CD/DVD readers.

IEB Extension — Compton Scattering, de Broglie & Heisenberg

Compton scattering: When a high-energy photon (X-ray/gamma ray) collides with a free electron, the photon loses energy and its wavelength increases (Δλ = h/mc × (1 − cosθ)). This momentum transfer proves photons behave as particles with momentum p = h/λ = hf/c.

de Broglie wavelength calculations: An electron (m = 9.11 × 10⁻³¹ kg) moving at v = 2 × 10⁶ m/s has λ = h/mv = 6.63×10⁻³⁴ / (9.11×10⁻³¹ × 2×10⁶) = 3.64 × 10⁻¹⁰ m — in the X-ray range, confirmed by electron diffraction experiments.

Heisenberg Uncertainty Principle (qualitative): It is impossible to simultaneously know both the exact position and exact momentum of a particle: Δx·Δp ≥ h/4π. This is not a measurement error — it is a fundamental property of quantum systems. The more precisely we know position, the less precisely we can know momentum, and vice versa.

Show all working. Use h = 6.63 × 10⁻³⁴ J·s, c = 3 × 10⁸ m·s⁻¹, e = 1.6 × 10⁻¹⁹ C.

Question 1

Yellow light has a wavelength of 590 nm. (a) Calculate the frequency of this light. (b) Calculate the energy of one photon of yellow light in joules. (c) Convert your answer to electron-volts (1 eV = 1.6 × 10⁻¹⁹ J).

Question 2

The threshold frequency of calcium metal is 7.73 × 10¹⁴ Hz. (a) Calculate the work function of calcium in joules. (b) Light of frequency 9.0 × 10¹⁴ Hz shines on the calcium surface. Will electrons be ejected? Justify your answer. (c) Calculate the maximum kinetic energy of the ejected electrons.

Question 3

UV light of frequency 1.2 × 10¹⁵ Hz shines on a metal surface with work function 3.8 × 10⁻¹⁹ J. (a) Calculate the maximum kinetic energy of photoelectrons. (b) If the intensity of the UV light is doubled but the frequency remains the same, describe and explain what happens to: (i) the number of electrons emitted per second, and (ii) the maximum kinetic energy of each emitted electron.

Question 4

Arrange the following electromagnetic waves in order of increasing energy per photon, and give one use for each: (a) gamma rays, (b) radio waves, (c) infrared radiation, (d) X-rays, (e) visible light. Explain the connection between frequency and energy per photon.

Question 5

A hot gas of hydrogen emits light at specific wavelengths (an emission spectrum). When cool hydrogen gas is placed in front of a white light source, an absorption spectrum is observed. (a) Explain why emission and absorption spectra occur at the same wavelengths. (b) How do scientists use spectra to identify elements in distant stars? (c) What does the spacing between spectral lines tell us about the energy levels in an atom?

Question 6

In a photoelectric effect experiment on an unknown metal, light of different frequencies (all above the threshold) was shone on the metal, and the maximum kinetic energy of the ejected photoelectrons was measured:

Frequency, f (×10¹⁴ Hz)	Ek(max) (×10⁻¹⁹ J)
6.0	0.66
8.0	1.99
10.0	3.31
12.0	4.64

(a) Using the first and last data points, calculate the gradient of a graph of Ek(max) (y-axis) against f (x-axis). Which physical constant does this gradient represent? (3 marks)
(b) Using your gradient and any one data point, calculate the x-intercept of the graph (i.e. the threshold frequency f₀ for this metal). (2 marks)
(c) Hence calculate the work function W of this metal. (2 marks)

Nature of Electromagnetic Radiation

The Electromagnetic Spectrum

The Photoelectric Effect

Emission and Absorption Spectra

Wave-Particle Duality and Lasers

Photoelectric Effect Simulator