Radio waves and gamma rays are the same thing travelling at the same speed. The only difference between them is how tightly the wave is packed — and that single difference decides whether the radiation warms your dinner or goes through your bones.
📚 What you need to know
The electromagnetic spectrum covers all electromagnetic radiation, from radio waves to gamma rays.
Wavelength (λ) is the distance between two peaks; frequency (f) is how many waves pass per second.
All electromagnetic radiation travels at the speed of light, c = 3.00 × 108 m s−1 in a vacuum.
c = fλ, so frequency and wavelength are inversely proportional.
E = hf, so higher frequency means higher energy per photon.
Short wavelength means high frequency and high energy — UV, X-rays and gamma rays.
A continuous spectrum contains every frequency; a line spectrum contains only certain ones.
One speed, many wavelengths
Every kind of electromagnetic radiation moves at the same speed through a vacuum. Since the speed is fixed, squeezing more waves into each second means each wave has to be shorter. That is the whole content of c = fλ.
The two equations you need
c = fλ and E = hf
c = 3.00 × 108 m s−1, h = 6.63 × 10−34 J s
Count the peaks. The lower wave fits four times as many into the same width, so its frequency is four times higher and its photons carry four times the energy.
The regions of the spectrum
The regions have no sharp edges; they shade into one another. What matters for chemistry is the energy per photon, and that rises steadily from left to right.
Notice what makes radiation dangerous. It is not how much of it there is, but how much energy each individual photon carries. A bright red lamp delivers vast numbers of low-energy photons and none of them can break a bond; a faint UV source delivers few photons, but each one has enough energy to do damage. Intensity and photon energy are completely separate things.
Continuous and line spectra
Pass white light through a prism and you get a continuous spectrum: every frequency is present and the colours run into each other with no gaps. Pass light emitted by an excited gas through the same prism and you get something startling — a handful of sharp coloured lines with darkness in between.
The black regions in the lower spectrum are the important part. If an atom could emit any energy at all, that strip would look exactly like the one above it.
This is where the word quantised comes from. A quantum is a fixed packet, and a line spectrum says an atom releases energy only in specific packet sizes — never anything in between. That observation is the reason the whole model of energy levels exists.
WORKED EXAMPLE
Red light has a wavelength of 700 nm. Calculate its frequency and the energy of one photon.
Convert the wavelength to metres700 nm = 700 × 10−9 = 7.00 × 10−7 mEvery one of these questions starts here. Working in nanometres is the single most common source of a wrong answer.Rearrange c = fλ for frequencyf = c ÷ λ = 3.00 × 108 ÷ 7.00 × 10−7f = 4.29 × 1014 s−1Now use E = hfE = 6.63 × 10−34 × 4.29 × 1014E = 2.84 × 10−19 J per photon
WORKED EXAMPLE
Violet light has a wavelength of 400 nm. Show that its photons carry more energy than red light at 700 nm, and find how many times more.
Frequency of violet lightf = 3.00 × 108 ÷ 4.00 × 10−7 = 7.50 × 1014 s−1Energy per photonE = 6.63 × 10−34 × 7.50 × 1014 = 4.97 × 10−19 JCompare with red4.97 ÷ 2.84 = 1.75violet photons carry 1.75 times the energyThe shortcut worth noticingSince E is proportional to 1/λ, the energy ratio is just the inverse wavelength ratio: 700 ÷ 400 = 1.75. Same answer without touching h or c.
WORKED EXAMPLE
Explain what a line spectrum tells you about the electrons in an atom that a continuous spectrum does not.
What is actually seenOnly certain frequencies appear, separated by darkness, rather than an unbroken band of colour.What each line meansSince E = hf, a fixed frequency means a fixed energy. Each line is one exact amount of energy being released by the atom.What follows about the electronsIf only certain energies can be emitted, the electron can only have moved between certain fixed energy values. Energies in between are not available.electron energies are quantised, not continuousTurn the argument round to check it. If electrons could hold any energy at all, every possible transition would exist and the spectrum would be continuous.
💡 Exam tip
Convert nm to m before substituting into c = fλ. Multiply by 10−9.
Both equations are in the data booklet, along with c and h — you do not need to memorise them.
Say frequency and wavelength are inversely proportional, not just “opposite”.
Link high frequency to high energy through E = hf every time you are asked why UV is harmful.
Describe a line spectrum as evidence that energy is quantised.
Give answers in standard form with the correct unit: s−1 for frequency, J for energy.
⚠️ Common mix-up
Leaving the wavelength in nanometres, which puts the answer out by a factor of 109.
Saying high energy radiation travels faster. All of it travels at c.
Confusing intensity with photon energy — brighter is not the same as more energetic.
Thinking visible light is most of the spectrum. It is a very narrow strip.
Describing a line spectrum as “a spectrum with lines missing”, when it is the reverse.
Up next: Atomic Emission Spectra — you have seen that atoms emit only fixed frequencies. The next page explains what the electrons are doing to produce each line, and why the lines crowd together at one end.
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