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medium difficulty10 min

Photon: Particle Nature of Light

A photon is a discrete packet, or quantum, of electromagnetic radiation that carries energy E = h nu and momentum p = h/λ while moving with the speed of light in vacuum.

In one line: Photon energy follows frequency; photon momentum follows wavelength.

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Understand it

  • The photon model explains interactions where light transfers energy in fixed packets rather than continuously.
  • In the photoelectric effect, the energy of one photon is given to one electron.
  • A photon has no rest mass, but it has energy and momentum because it is radiation in motion.
  • The energy depends on frequency, so higher-frequency light has more energetic photons.

Example

Blue light has a higher frequency than red light, so each blue photon carries more energy than each red photon. This is why frequency decides whether photoelectric emission can occur for a given metal.

Formula and rule

Photon energy: E = h nu = hc/λ.

Photon momentum: p = h/λ = E/c. h is in J s, nu in Hz, c in m s−1, λ in m, E in J, and p in kg m s−1.

Use these formulas for radiation quanta, photoelectric effect, and photon momentum calculations.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

Find the energy of a photon of wavelength 600 nm.

  1. 1Convert λ = 600 × 10−9 m.
  2. 2E = hc/λ = (6.63 × 10−34)(3.0 × 108)/(600 × 10−9) = 3.315 × 10−19 J, which is about 2.07 eV.
  3. 3This photon is less energetic than a photon of shorter wavelength.

Method you can reuse

Identify whether frequency or wavelength is given, use E = h nu or E = hc/λ, convert nanometre to metre if needed, find momentum using p = h/λ or E/c, and interpret higher frequency as higher photon energy.

Visual tip

A simple photon packet sketch may show direction of propagation, wavelength, and energy transfer to an electron. Label photon, direction of travel, wavelength, and absorbing electron if linked to photoelectric effect.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

How can a photon have momentum if it has no rest mass?

Think first, then show answer
A photon has no rest mass, but it carries energy as electromagnetic radiation. Its momentum is given by p = h/λ, so photon momentum is linked with wavelength, not with the classical formula mv for massive particles at rest.

Common wrong answer

Wrong: Increasing intensity increases energy of each photon. Correct: Increasing intensity increases the number of photons crossing an area per second; energy of each photon depends on frequency.

Don't mix this up

A frequent mistake is saying that a photon has rest mass because it has momentum. At this level, a photon is treated as having zero rest mass but non-zero energy and momentum.

Exam tip

Use photon language when the question involves emission, absorption, photoelectric effect, or momentum of radiation. Use wave language when the question is about wavelength and frequency propagation, but connect both through E = h nu and p = h/λ.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Asked in direct formula numericals, conceptual comparisons of red and violet light, explanation of photoelectric effect, and assertion-reason questions on particle nature of radiation.
  1. 1

    Enough for 1 mark

    A photon is a discrete packet, or quantum, of electromagnetic radiation that carries energy E = h nu and momentum p = h/λ while moving with the speed of light in vacuum.

  2. 2

    Add for 2 marks

    Example: Blue light has a higher frequency than red light, so each blue photon carries more energy than each red photon. This is why frequency decides whether photoelectric emission can occur for a given metal.

  3. 3

    Add for 3 marks

    The photon model explains interactions where light transfers energy in fixed packets rather than continuously.

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