Mistake Master
Properties of photons
Light is not just a wave; it comes in packets called photons, each carrying a fixed amount of energy set by its frequency. One equation, E = hν, is the whole story — and it inverts the same way the spectrum does.
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Light in packets.
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Light is quantized into particles called photons. Each photon carries an energy fixed by its frequency: E = hν, where h is Planck's constant. Because frequency and wavelength are linked (c = λν), you can also write E = hc/λ.
So a higher-frequency (and thus shorter-wavelength) photon carries more energy. This is the same ordering as the whole spectrum, now applied to a single packet of light.
The photon picture explains why matter absorbs and emits light in specific amounts: an electron gains or loses exactly the energy of one photon, not a continuous trickle.
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Working with photon energy.
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Use E = hν = hc/λ and keep the direction of each relationship.
- Relate energy to frequency. E = hν: energy is directly proportional to frequency.
- Relate energy to wavelength. E = hc/λ: energy is inversely proportional to wavelength.
- Compare two photons. Higher frequency or shorter wavelength → more energy per photon.
- Connect to matter. An electron absorbs or emits a photon whose energy matches an allowed energy change — a discrete amount.
§3
The pieces you'll meet.
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One equation, two forms.
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Worked example: which photon is more energetic?
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Question. Photon A is blue light (short wavelength); photon B is red light (longer wavelength). Which carries more energy?
Use E = hc/λ. Energy is inversely proportional to wavelength. Blue light has the shorter wavelength.
Conclusion. The blue photon (shorter λ, higher frequency) carries more energy than the red photon.
Consistency. This matches E = hν too: blue light has the higher frequency, so the higher energy. Both forms of the equation agree because c = λν links them.
§5
Mistakes that cost real points.
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"A longer-wavelength photon has more energy."
Photon energy is inversely proportional to wavelength (E = hc/λ), so a longer wavelength means a lower-energy photon. Red light photons carry less energy than blue; radio photons less than X-ray. The relationship is the same inversion as the whole spectrum.
Fix. Use E = hc/λ: longer wavelength, lower energy. Only frequency and energy rise together.
"Brighter light means each photon has more energy."
Brightness (intensity) is about how many photons arrive, not the energy of each one. A single photon's energy depends only on its frequency (E = hν). Dim blue light still has more-energetic photons than bright red light.
Fix. Separate per-photon energy (set by frequency) from intensity (set by the number of photons).
"Energy is absorbed continuously, in any amount."
Matter absorbs and emits light in discrete photon-sized amounts, not a continuous trickle. An electron changes energy by exactly one photon's worth, which is why atoms absorb and emit specific wavelengths.
Fix. Treat light-matter energy exchange as quantized: whole photons, matching allowed energy changes.
§6
Skill Check.
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Ten scenarios. Pick the chips that match your answer, then check. A scenario marks complete the first time every part is right. Progress saves on this device.