• In classical wave theory, electromagnetic (EM) radiation is assumed to behave as a?wave
  • This is demonstrated by the fact EM radiation exhibits phenomena such as?diffraction?and?interference

• However, experiments from the last century, such as discovering the?photoelectric effect?and atomic line spectra, can only be explained if the EM radiation is thought of as behaving as?particles

• These experiments have formed the basis of?quantum theory, which will be explored in detail in this section

Photons

• Photons are fundamental particles which make up all forms of electromagnetic radiation
• A photon is defined as

A massless ''packet'' or a ''quantum'' of electromagnetic energy

A wave packet (photon)

• This means is that the energy of a photon is not transferred continuously, but as?discrete?packets of energy
• In other words, each photon carries a specific amount of energy, and transfers this energy all in one go, rather than supplying a consistent amount of energy
• The energy of a photon can be calculated using the formula:Where:

• • E?= energy of the photon (J)
  • h?=?Planck's constant?(J s)
  • c?=?the speed of light?(m s-1)
  • f?= frequency in Hertz (Hz)
  • λ?= wavelength (m)

• This equation tells us:
  • The higher the frequency of EM radiation, the higher the energy of the photon
  • The energy of a photon is inversely proportional to the wavelength
  • A long-wavelength photon of light has a lower energy than a shorter-wavelength photon

Step 1: Write down the known quantities

• • Wavelength, λ = 490 nm = 490 × 10?9?m
  • Power,?P?= 3.6 mW = 3.6 × 10?3?W
  • Time,?t?= 2.0 s

Step 2: Write the equations for wave speed and photon energyPhoton Momentum

• Einstein showed that a photon travelling in a vacuum has momentum, despite it having no mass
• The momentum (p) of a photon is related to its energy (E) by the equation:

• Where
  • c =?the speed of light
  • p = the momentum of the photon (kg m s-1)
  • E = the energy of the photon (J)

Step 1: Write down the known quantities

• • Power,?P?= 5.0 mW = 5.0 × 10?3?W
  • Frequency,?f?= 5.6 × 1014?Hz
  • Cross-sectional area,?A?= 8.0 × 10?6?m2

Step 2: Write the equations for photon energy and momentumExam Tip