The Photon (CIE A Level Physics)

• 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 the photoelectric effect and atomic line spectra, can only be explained if EM radiation is assumed to behave as particles
• These experiments have formed the basis of quantum theory, which will be explored in detail in this section

• Photons are fundamental particles which make up all forms of electromagnetic radiation
• A photon is a massless “packet” or a “quantum” of electromagnetic energy
• What this means is that the energy 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:

E = hf

• Using the wave equation, energy can also be equal to:

• 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 energy

Step 3: Calculate the energy of one photon

Step 4: Calculate the number of photons hitting the surface every second

Step 5: Calculate the number of photons that hit the surface in 2 s

(8.9 × 10¹⁵) × 2 = 1.8 × 10¹⁶

• 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 is the speed of light

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 momentum

photon energy:   E = hf

Step 3: Calculate the photon momentum

Step 4: Calculate the number of photons incident on the plate every second

Step 5: Calculate the force exerted on the plate in a 1.0 s time interval

Force  =  rate of change of momentum

= number of photons per second × momentum of each photon

= (1.35 × 10¹⁶) × (1.24 × 10^-27)

= 1.67 × 10^-11 N

 Step 6: Calculate the pressure