Photons and the equation E = hf

Overview

Recall questions on what a photon is, E = hf and its wavelength form with the value of the Planck constant, the electronvolt and conversions to joules, worked photon-energy calculations, comparing red with blue and gamma with radio photons, the number of photons a laser emits each second, and why the graininess of light is not obvious.

What you need to know

Answer each one before you reveal it.

Questions from this subtopic

Each one with the model answer underneath.

1. 1

   What is a photon?

   Model answer

   A photon is a quantum of electromagnetic radiation, a discrete packet of energy that carries a fixed amount of energy determined by the frequency of the radiation.

2. 2

   State the equation for the energy of a photon, defining each symbol with its unit.

   Model answer

   E = hf, where E is the photon energy in joules, h is the Planck constant in J s and f is the frequency of the radiation in hertz.

3. 3

   State the value of the Planck constant with its unit.

   Model answer

   The Planck constant is 6.63 × 10⁻³⁴ J s.

4. 4

   Write the photon energy equation in terms of wavelength, defining each symbol.

   Model answer

   E = hc/λ, where E is the photon energy in joules, h is the Planck constant in J s, c is the speed of light in a vacuum in m s⁻¹ and λ is the wavelength in metres.

5. 5

   Calculate the energy of a photon of frequency 6.0 × 10¹⁴ Hz.

   Model answer

   E = hf = 6.63 × 10⁻³⁴ × 6.0 × 10¹⁴ = 4.0 × 10⁻¹⁹ J, and 3.98 × 10⁻¹⁹ J ÷ 6.63 × 10⁻³⁴ J s returns 6.0 × 10¹⁴ Hz as given.

6. 6

   Calculate the energy of a photon of wavelength 450 nm in joules and in electronvolts.

   Model answer

   E = hc/λ = (6.63 × 10⁻³⁴ × 3.00 × 10⁸)/4.50 × 10⁻⁷ = 4.42 × 10⁻¹⁹ J, which is 4.42 × 10⁻¹⁹ / 1.60 × 10⁻¹⁹ = 2.76 eV, and hc ÷ 4.42 × 10⁻¹⁹ J returns 4.50 × 10⁻⁷ m.

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