Unit 3 · Topic 3.12 Beta

Properties of Photons

Light travels at c = λν, so wavelength and frequency are inversely related.

Practice 5: Mathematical Routines

Question set for this topic

Part 1 · Hook

Why this matters

Only ultraviolet light gives you a sunburn. Hours under a red lamp will not, no matter how bright it is. The reason is that light comes in packets, and what matters is the energy of each packet, which you can calculate from its wavelength.

Part 2 · Before you start

What this builds on

Part 3 · Prerequisite check

Quick check before you start

1. Which carries more energy per photon?

  1. Ultraviolet
  2. Infrared
  3. Microwave
Show the answer

Shorter wavelengths carry more energy per photon.

  • Correct: Ultraviolet:
  • Infrared:
  • Microwave:

2. What is 500 nm in meters?

  1. 5.00 × 10⁻⁷ m
  2. 5.00 × 10⁻⁹ m
  3. 5.00 × 10² m
Show the answer

500 × 10⁻⁹ m = 5.00 × 10⁻⁷ m.

  • Correct: 5.00 × 10⁻⁷ m:
  • 5.00 × 10⁻⁹ m:
  • 5.00 × 10² m:

3. How many particles are in one mole?

  1. 6.022 × 10²³
  2. 6.626 × 10⁻³⁴
  3. 2.998 × 10⁸
Show the answer

Avogadro's number.

  • Correct: 6.022 × 10²³:
  • 6.626 × 10⁻³⁴:
  • 2.998 × 10⁸:

Part 4 · See it

See it first

Red light at 700 nm has a longer wavelength and lower frequency than violet light at 400 nm, so each red photon carries less energy. A photon is absorbed only when its energy, hν, equals the gap between two energy levels.
Shorter wavelength means higher frequency and more energy per photon; absorption needs a photon matching the gap. LevlPrep original diagram.

Part 5 · Step by step

How it works, step by step

  1. All light travels at c = 2.998 × 10⁸ m/sc = λν, so wavelength and frequency are inversely proportional
  2. Each photon carries energy E = hνshorter wavelength, higher frequency, more energy per photon: E = hc/λ
  3. Energy levels in atoms and molecules are quantizedonly photons whose energy matches a gap are absorbed or emitted
  4. Each element has its own set of gapseach emits its own set of wavelengths, a line spectrum

Part 6 · Key ideas

Key ideas

  • c = λν with c = 2.998 × 10⁸ m/s; λ in meters (1 nm = 10⁻⁹ m).
  • E = hν = hc/λ with h = 6.626 × 10⁻³⁴ J·s. This is one photon, in joules.
  • Per mole: multiply by 6.022 × 10²³, then divide by 1000 for kJ/mol.
  • A photon is absorbed or emitted only when its energy equals a gap between levels.

Part 7 · Misconception

A common mistake

The wrong idea: Brighter light has more energy per photon, so a bright enough lamp of any color can cause any transition.

What actually happens: Brightness is the number of photons. Energy per photon depends only on frequency (E = hν), so each photon must match the gap on its own.

Part 8 · Check yourself

Check yourself

Exam-style questions. Anything you miss goes into your review queue.

Data table

Emission lines of a gas discharge tube

A student views the light from a tube of hot hydrogen gas through a spectroscope and records four bright lines in the visible region.

Visible emission lines
LineWavelength (nm)Color
A656.3red
B486.1blue-green
C434.0blue-violet
D410.2violet

1. What is the frequency of line A?

Type a number in s⁻¹.

Show the answer

λ = 656.3 nm = 6.563 × 10⁻⁷ m. ν = c/λ = (2.998 × 10⁸ m/s) / (6.563 × 10⁻⁷ m) = 4.56803 × 10¹⁴ s⁻¹, which is 4.568 × 10¹⁴ s⁻¹.

  • Answer: 4.568 × 1014 s⁻¹

2. What is the energy of one photon of line A?

  1. 3.03 × 10⁻¹⁹ J
  2. 4.35 × 10⁻⁴⁰ J
  3. 1.82 × 10⁵ J/mol
  4. 3.03 × 10⁻²⁸ J
Show the answer

E = hc/λ = (6.626 × 10⁻³⁴ J·s)(2.998 × 10⁸ m/s) / (6.563 × 10⁻⁷ m) = 3.03 × 10⁻¹⁹ J.

  • Correct: 3.03 × 10⁻¹⁹ J: Right: E = hc/λ with λ in meters.
  • 4.35 × 10⁻⁴⁰ J: This is hλ. Energy is E = hν = hc/λ, which falls as λ rises.
  • 1.82 × 10⁵ J/mol: This is the energy of a mole of photons; one photon is 6.022 × 10²³ times smaller.
  • 3.03 × 10⁻²⁸ J: This used λ in nm. Convert first: 656.3 nm = 6.563 × 10⁻⁷ m.

3. Which line comes from the largest drop in energy between two levels?

  1. A, 656.3 nm
  2. B, 486.1 nm
  3. C, 434.0 nm
  4. D, 410.2 nm
Show the answer

E = hc/λ, so the shortest wavelength carries the most energy. Line D, at 410.2 nm, comes from the largest energy drop.

  • A, 656.3 nm: Line A has the longest wavelength, so the smallest energy drop of the four.
  • B, 486.1 nm: Line B, at 486.1 nm, is a longer wavelength than two of the other lines.
  • C, 434.0 nm: Line C, at 434.0 nm, is longer than the 410.2 nm line.
  • Correct: D, 410.2 nm: Right: shortest wavelength, most energy.

4. Why does hydrogen emit only these particular wavelengths rather than a continuous rainbow?

  1. Its electron energies are quantized, so only photons matching the gaps between levels are emitted.
  2. Its electrons can sit at any energy, but the spectroscope filters out the other wavelengths.
  3. Hydrogen atoms are too small to emit light of any other color than these four.
  4. Hot hydrogen gas reflects these four colors from the light in the room.
Show the answer

Electrons in an atom occupy fixed levels. A drop from one level to another emits a photon whose energy, and so wavelength, equals that gap exactly. A few gaps give a few lines.

  • Correct: Its electron energies are quantized, so only photons matching the gaps between levels are emitted.: Right: fixed levels, fixed photon energies.
  • Its electrons can sit at any energy, but the spectroscope filters out the other wavelengths.: A spectroscope spreads light out; it would show a continuous spectrum if one were emitted.
  • Hydrogen atoms are too small to emit light of any other color than these four.: Atom size does not pick the colors; the gaps between levels do.
  • Hot hydrogen gas reflects these four colors from the light in the room.: The light is emitted by the hot gas, not reflected.

5. When the wavelength of light is doubled, what happens to its frequency and to the energy of each photon?

  1. Both are halved.
  2. Both are doubled.
  3. Frequency halves; energy doubles.
  4. Frequency doubles; energy halves.
Show the answer

c = λν with c fixed, so doubling λ halves ν. E = hν, so the energy halves too.

  • Correct: Both are halved.: Right: c fixed, E ∝ ν.
  • Both are doubled.: Longer waves have lower frequency and less energy.
  • Frequency halves; energy doubles.: E is proportional to ν, so they change together.
  • Frequency doubles; energy halves.: Doubling λ lowers ν, not raises it.

6. Put the steps for finding the energy of one mole of photons from a wavelength in nm in order.

  1. Convert the wavelength from nm to m
  2. Calculate the frequency, ν = c/λ
  3. Calculate the energy of one photon, E = hν
  4. Multiply by Avogadro's number to get J/mol
  5. Convert J/mol to kJ/mol
Show the answer

Units first, then frequency, then energy per photon, then per mole, then kJ.

  • Correct order: 1. Convert the wavelength from nm to m 2. Calculate the frequency, ν = c/λ 3. Calculate the energy of one photon, E = hν 4. Multiply by Avogadro's number to get J/mol 5. Convert J/mol to kJ/mol

Part 9 · Summary

Summary

Light travels at c = λν, so wavelength and frequency are inversely related. Each photon carries E = hν = hc/λ joules, and a mole of photons carries 6.022 × 10²³ times that. Energy levels are quantized, so atoms and molecules absorb or emit only photons whose energy equals a gap between levels.

Part 10 · Up next

What comes next

Part 11 · Connections

Connections