Master AP Chemistry Topic 3.11 with this free practice quiz. Test your skills on microwave spectroscopy, infrared spectroscopy, and uv vis spectroscopy to prepare for your AP exam.
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The Spectrum, in Order
All electromagnetic radiation travels at c = 3.00 × 10⁸ m/s in a vacuum. Ordered from longest wavelength to shortest: radio, microwave, infrared, visible, ultraviolet, X-ray, gamma.
Frequency and photon energy run in the opposite direction to wavelength. Radio waves have the longest wavelength, the lowest frequency and the weakest photons. Gamma rays have the shortest wavelength, the highest frequency and the most energetic photons.
Visible light is a narrow slice in the middle, roughly 400 nm to 700 nm. Violet (~400 nm) is the high energy end; red (~700 nm) is the low energy end. Anything just below 400 nm is ultraviolet, anything just above 700 nm is infrared.
The Two Equations
c = λν
Wavelength λ (in metres) times frequency ν (in s⁻¹, also written Hz) equals the speed of light. Because c is fixed, λ and ν are locked in inverse proportion: halve the wavelength and the frequency doubles.
E = hν = hc/λ
A photon’s energy is E = hν, where h is Planck’s constant, 6.626 × 10⁻³⁴ J·s. Substituting ν = c/λ gives E = hc/λ, the form you will use most, because spectra are reported in wavelengths. Energy rises as wavelength falls.
Two consequences worth fixing in memory. Photon energies are tiny, around 10⁻¹⁹ J for visible light, so questions often ask for energy per mole instead: multiply by Avogadro’s number, 6.022 × 10²³. And the product hc is a constant, 1.986 × 10⁻²⁵ J·m, which speeds up every E = hc/λ calculation.
What Each Region Does to Matter
The region of the spectrum tells you what kind of change the radiation causes. This matching is a favourite AP question.
Microwave radiation is absorbed by molecules rotating. The photon energy is small, enough only to change rotational states.
Infrared radiation makes bonds vibrate, stretching and bending. Each type of bond absorbs at characteristic frequencies, which is why IR spectra are used to identify the bonds and functional groups present in a sample.
Ultraviolet and visible radiation move electrons between energy levels. Absorbing a photon promotes an electron to a higher level; when the electron falls back, it emits a photon with exactly the energy of the gap.
That last point explains line spectra. Electron energy levels are quantized, so only certain gaps exist, and each gap gives one line of one specific colour or wavelength. Every element has its own set of gaps, so every element’s emission spectrum is a unique fingerprint.
Worked Examples
Example 1: photon energy at 450 nm
E = hc/λ = (6.626 × 10⁻³⁴ × 3.00 × 10⁸) / (450 × 10⁻⁹) = 4.42 × 10⁻¹⁹ J per photon.
Per mole: 4.42 × 10⁻¹⁹ × 6.022 × 10²³ = 2.66 × 10⁵ J/mol, or 266 kJ/mol. Blue light therefore carries enough energy per mole to matter chemically, unlike radio waves, whose photons are millions of times weaker.
Example 2: from energy back to wavelength
An electron transition emits a photon of 3.03 × 10⁻¹⁹ J. Find the wavelength and the colour.
λ = hc/E = (1.986 × 10⁻²⁵) / (3.03 × 10⁻¹⁹) = 6.56 × 10⁻⁷ m = 656 nm.
656 nm sits in the red part of the visible spectrum. This is in fact hydrogen’s red emission line, the gap between its third and second energy levels.
Traps Specific to This Topic
Forgetting the nanometre conversion is the costliest error here. If λ is given in nm, convert to metres (× 10⁻⁹) before using either equation, or your answer is out by a factor of 10⁹.
Read whether the question wants energy per photon or per mole. They differ by a factor of 6.022 × 10²³, and both versions appear as answer options.
Longer wavelength means lower energy, never higher. When a question asks you to rank radiations by energy, reverse the wavelength order.
Emission and absorption involve the same gap, so the photon has the same energy either way. Falling electrons emit; rising electrons absorb. Direction questions test exactly this.
Frequency is never measured in metres and wavelength never in s⁻¹. If your calculated ν comes out in anything but s⁻¹, a unit conversion has gone wrong upstream.