Topic 3.12 Notes – Properties of Photons

1. What a Photon Is

A photon is a discrete packet (quantum) of electromagnetic energy.

Light shows wave-particle duality, meaning it behaves in two ways:

• As a wave
  • Described by wavelength $\lambda$ (meters)
  • Described by frequency $\nu$ (s⁻¹ or Hz)
• As a particle
  • Made of photons
  • Each photon carries a specific, fixed amount of energy

The key idea is that energy is quantized.

• Atoms and molecules cannot absorb “any amount” of energy.
• They absorb or emit energy in specific chunks.
• Each chunk corresponds exactly to the energy of one photon.

Two constants you must know (from the reference sheet):

• $c = 2.998 \times 10^{8} \, \text{m/s}$ (speed of light)
• $h = 6.626 \times 10^{-34} \, \text{J}\\cdot\\text{s}$ (Planck’s constant)

Those constants tie the wave description of light to its energy.

2. The Mathematical Relationships You Must Know

These equations are often used together in one problem.

Wave relationship

$$c = \lambda \nu$$

• $c$ = speed of light
• $\lambda$ = wavelength
• $\nu$ = frequency

Since $c$ is constant, wavelength and frequency are inversely related:

• Shorter $\lambda$ → higher $\nu$
• Longer $\lambda$ → lower $\nu$

So UV light (very short wavelength) has a very high frequency. Radio waves (long wavelength) have low frequency.

Energy of a photon

$$E = h\nu$$

• $E$ = energy of one photon (J)
• $h$ = Planck’s constant
• $\nu$ = frequency

Since $\nu = \frac{c}{\lambda}$, we often combine them:

$$E = \frac{hc}{\lambda}$$

Now you can see the full relationship:

• Higher frequency → higher energy
• Shorter wavelength → higher energy

If a problem gives wavelength, you’ll usually:

1. Convert nm to meters.
2. Use $E = \frac{hc}{\lambda}$.

Be careful with units. Missed unit conversions are one of the most common point losses.

3. Electronic Transitions in Atoms and Molecules

Electrons exist in quantized energy levels. They cannot exist between levels.

When light interacts with an atom, one photon interacts with one electron.

Absorption

• A photon is absorbed.
• The electron jumps to a higher energy level (excited state).
• The atom’s energy increases by exactly:

$$\Delta E = +h\nu$$

The photon must match the exact energy gap between levels. If it doesn’t match, nothing happens.

Emission

• An electron falls from a higher level to a lower one.
• A photon is emitted.
• The atom’s energy decreases by:

$$\Delta E = -h\nu$$

The energy of the emitted photon equals the energy difference between the two levels.

Bigger gap between levels → higher-energy photon → higher frequency → shorter wavelength.

That’s why different elements produce different line spectra. Their energy levels are unique.

On FRQs, when they ask you to explain a color of light emitted, they want you to say the photon energy equals the difference between two quantized energy levels.

4. The Photoelectric Effect

This is the strongest evidence that light behaves like particles.

When light shines on a metal:

• Electrons are ejected only if the frequency is above a certain minimum, called the threshold frequency.

The energy relationship is:

$$h\nu = \text{binding energy} + \text{kinetic energy}$$

• Binding energy = energy needed to remove the electron.
• Extra energy becomes kinetic energy of the ejected electron.

Three observations matter:

• If frequency is below threshold → no electrons are ejected, even if intensity is high.
• Increasing frequency (above threshold) → increases kinetic energy.
• Increasing intensity (above threshold) → increases number of electrons ejected.

The AP loves testing this distinction. Frequency controls energy per photon. Intensity controls number of photons.