NSWPhysicsSyllabus dot point

Inquiry Question 1: What is light?

Describe the electromagnetic spectrum in terms of frequency, wavelength and photon energy, and outline how Maxwell's equations conceptually predict electromagnetic waves travelling at the speed of light

Q: 2022 HSC HSC: A radio station broadcasts at 102.5 MHz, and a medical X-ray machine produces photons of wavelength $5.0 \times 10^{-11}$ m. Calculate the wavelength of the radio waves and the energy of one X-ray photon in joules and in electron-volts.

Radio wavelength from $c = f \lambda$: $\lambda = c / f = 3.00 \times 10^8 / (102.5 \times 10^6) = 2.93$ m. X-ray photon frequency: $f = c / \lambda = 3.00 \times 10^8 / (5.0 \times 10^{-11}) = 6.0 \times 10^{18}$ Hz. Photon energy ($h = 6.626 \times 10^{-34}$ J s): $E = h f = 6.626 \times 10^{-34} \times 6.0 \times 10^{18} = 4.0 \times 10^{-15}$ J. In electron-volts ($1$ eV $= 1.602 \times 10^{-19}$ J): $E = 4.0 \times 10^{-15} / 1.602 \times 10^{-19} = 2.5 \times 10^{4}$ eV $= 25$ keV. Markers reward correct use of $c = f \lambda$, $E = hf$, and unit conversion to eV. The X-ray photon has roughly $10^{19}$ times the energy of the radio photon, which is why X-rays ionise tissue and radio waves do not.

A focused answer to the HSC Physics Module 7 dot point on the electromagnetic spectrum. Frequency, wavelength and photon energy across radio to gamma rays, the relations c = f lambda and E = hf, and how Maxwell's equations conceptually predict EM waves at the speed of light.

Generated by Claude OpusReviewed by Better Tuition Academy8 min answerUpdated 2026-05-18

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What this dot point is asking

NESA wants you to know the layout of the electromagnetic spectrum, the relationships $c = f \lambda$ and $E = hf$ , and the historical and conceptual significance of Maxwell's equations. You should be able to identify each band of the spectrum, compare wavelengths, frequencies and photon energies across the bands, and explain why Maxwell's prediction unified optics and electromagnetism.

The answer

The spectrum

Electromagnetic (EM) radiation is a transverse wave of oscillating electric and magnetic fields propagating at the speed of light, $c = 2.998 \times 10^8$ m/s in vacuum. The fields are perpendicular to each other and to the direction of propagation. EM waves do not need a medium.

The spectrum, ordered from longest wavelength to shortest:

Band	Wavelength (typical)	Frequency (typical)	Photon energy
Radio	IMATH_6 m	IMATH_7 MHz	IMATH_8 eV
Microwave	IMATH_9 mm to $1$ m	IMATH_11 MHz to $300$ GHz	IMATH_13 to $10^{-3}$ eV
Infrared	IMATH_15 nm to $1$ mm	IMATH_17 GHz to $430$ THz	IMATH_19 to $1.8$ eV
Visible	IMATH_21 to $700$ nm	IMATH_23 to $750$ THz	IMATH_25 to $3.1$ eV
Ultraviolet	IMATH_27 to $400$ nm	IMATH_29 THz to $30$ PHz	IMATH_31 to $124$ eV
X-ray	IMATH_33 pm to $10$ nm	IMATH_35 PHz to $30$ EHz	IMATH_37 eV to $124$ keV
Gamma	IMATH_39 pm	IMATH_40 EHz	IMATH_41 keV

Visible light runs from violet ( $\sim 400$ nm) to red ( $\sim 700$ nm). UV beyond about $10$ eV and X-rays ionise atoms; radio, microwave, infrared and most visible photons cannot.

Key relationships

For a wave of frequency $f$ and wavelength $\lambda$ travelling at speed $c$ :

c = f \lambda

The photon energy (the smallest "packet" of EM energy at frequency $f$ ) is:

E = h f = \frac{h c}{\lambda}

where $h = 6.626 \times 10^{-34}$ J s is Planck's constant. Higher-frequency, shorter-wavelength radiation carries more energy per photon.

Maxwell's equations, in words

By 1865, James Clerk Maxwell had combined four laws of electromagnetism into a self-consistent set:

Gauss's law for electricity. Electric field lines start on positive charges and end on negative charges; the total flux through a closed surface is proportional to the enclosed charge.
Gauss's law for magnetism. Magnetic field lines form closed loops; no magnetic monopoles exist.
Faraday's law of induction. A changing magnetic flux produces a circulating electric field (the EMF driving induced currents).
The Ampere-Maxwell law. A current and a changing electric flux both produce a circulating magnetic field. Maxwell's added term (the displacement current) was the key insight.

Together, items 3 and 4 say each kind of changing field creates the other. Combining them mathematically gives a wave equation for $\vec{E}$ and $\vec{B}$ that propagates at:

c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}

Substituting the static, table-book values $\mu_0 = 4\pi \times 10^{-7}$ T m/A and $\varepsilon_0 = 8.85 \times 10^{-12}$ F/m gives $c = 3.0 \times 10^8$ m/s. This matched mid-1800s measurements of the speed of light. Maxwell concluded that light is an EM wave, and that other wavelengths should exist. Hertz produced and detected radio waves in 1887, confirming the prediction.

What an EM wave looks like

At a snapshot in time, a plane EM wave travelling in the $+x$ direction has:

IMATH_56 oscillating sinusoidally in (say) the $y$ direction,
IMATH_58 oscillating in phase in the $z$ direction with $B_0 = E_0 / c$ ,
both perpendicular to the direction of propagation (transverse wave),
the wave carries energy and momentum but no rest mass.

The intensity (W m $^{-2}$ ) is proportional to $E_0^2$ .

Worked example: comparing energies

A green photon ( $\lambda = 550$ nm) and a UV photon ( $\lambda = 200$ nm):

Green: $E = h c / \lambda = (6.626 \times 10^{-34})(3.0 \times 10^8) / (5.5 \times 10^{-7}) = 3.6 \times 10^{-19}$ J $= 2.3$ eV.

UV: $E = (6.626 \times 10^{-34})(3.0 \times 10^8) / (2.0 \times 10^{-7}) = 9.9 \times 10^{-19}$ J $= 6.2$ eV.

The UV photon carries roughly $2.75$ times the energy of the green one. This is enough to break a typical chemical bond ( $\sim 4$ eV), which is why UV damages biological tissue.

Common traps

Confusing wavelength and frequency order. As wavelength increases, frequency decreases, and photon energy decreases.

Stating that EM waves need a medium. They do not; this is the difference from sound waves.

Quoting $c$ as the speed of light in glass. $c$ is the speed in vacuum. In glass, light slows by the refractive index, but the frequency stays the same.

Confusing $\mu_0$ and $\varepsilon_0$ . $\mu_0$ is the magnetic constant, $\varepsilon_0$ is the electric (permittivity) constant. Both are measured in entirely electrostatic and magnetostatic experiments.

Writing $E = hf$ but treating $E$ as the total wave energy. $E = hf$ is the energy of a single photon. Total wave energy depends on intensity and volume.

In one sentence

Electromagnetic radiation forms a single spectrum from radio to gamma rays related by $c = f \lambda$ and $E = hf$ , and Maxwell's equations predicted that mutually inducing oscillating $\vec{E}$ and $\vec{B}$ fields propagate at $c = 1/\sqrt{\mu_0 \varepsilon_0}$ , identifying light as an EM wave.

Past exam questions, worked

Real questions from past NESA papers on this dot point, with our answer explainer.

2022 HSC4 marksA radio station broadcasts at 102.5 MHz, and a medical X-ray machine produces photons of wavelength $5.0 \times 10^{-11}$ m. Calculate the wavelength of the radio waves and the energy of one X-ray photon in joules and in electron-volts.

Show worked answer →

Radio wavelength from $c = f \lambda$ :

$\lambda = c / f = 3.00 \times 10^8 / (102.5 \times 10^6) = 2.93$ m.

X-ray photon frequency:

$f = c / \lambda = 3.00 \times 10^8 / (5.0 \times 10^{-11}) = 6.0 \times 10^{18}$ Hz.

Photon energy ( $h = 6.626 \times 10^{-34}$ J s):

$E = h f = 6.626 \times 10^{-34} \times 6.0 \times 10^{18} = 4.0 \times 10^{-15}$ J.

In electron-volts ( $1$ eV $= 1.602 \times 10^{-19}$ J):

$E = 4.0 \times 10^{-15} / 1.602 \times 10^{-19} = 2.5 \times 10^{4}$ eV $= 25$ keV.

Markers reward correct use of $c = f \lambda$ , $E = hf$ , and unit conversion to eV. The X-ray photon has roughly $10^{19}$ times the energy of the radio photon, which is why X-rays ionise tissue and radio waves do not.

2019 HSC3 marksOutline how Maxwell's equations predicted that light is an electromagnetic wave.

Show worked answer →

Maxwell's equations unify the laws of electricity and magnetism into four field equations. The two relevant for wave prediction are:

Faraday's law: a changing magnetic field induces a circulating electric field.
The Ampere-Maxwell law: a changing electric field (the displacement current) induces a circulating magnetic field.

Together these say that a changing E-field generates a B-field, which in turn generates an E-field, and so on. Manipulating the equations yields a wave equation for both $\vec{E}$ and $\vec{B}$ with a propagation speed:

$c = 1 / \sqrt{\mu_0 \varepsilon_0}$

where $\mu_0$ and $\varepsilon_0$ are the magnetic and electric constants measured in static experiments. Substituting their measured values gives $c \approx 3.0 \times 10^8$ m/s, which matches Fizeau's and Foucault's measurements of the speed of light. Maxwell therefore concluded that light is an electromagnetic wave, and that other wavelengths of EM radiation should exist (later confirmed by Hertz's radio-wave experiments).

Markers reward the changing-field-induces-changing-field idea, the speed prediction from $\mu_0$ and $\varepsilon_0$ , and the agreement with measured $c$ .