Photon Energy (HL IB Physics)

The Photon Model

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

A massless “packet” or a “quantum” of electromagnetic energy

• This means that the energy transferred by a photon is not continuous 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
  • This is in contrast to waves which transfer energy continuously

Atomic Energy Levels

• Electrons in an atom occupy certain energy states called energy levels
  • Electrons will occupy the lowest possible energy level as this is the most stable configuration for the atom
  • When an electron absorbs or emits a photon, it can move between these energy levels, or be removed from the atom completely

Excitation

• When an electron moves to a higher energy level, the atom is said to be in an excited state
  • To excite an electron to a higher energy level, it must absorb a photon

• Electrons can also move back down to a lower energy level by de-excitation 
  • To de-excite an electron to a lower energy level, it must emit a photon

Ionisation

• When an electron is removed from an atom, the atom becomes ionised
  • An electron can be removed from any energy level it occupies
  • However, the ionisation energy of an atom is the minimum energy required to remove an electron from the ground state of an atom

Representing Energy Levels

• Energy levels can be represented as a series of horizontal lines
  • The line at the bottom with the greatest negative energy represents the ground state
  • The lines above the ground state with decreasing energies represent excited states
  • The line at the top, usually 0 V or infinity , represents the ionisation energy

Energy Levels in a Hydrogen Atom

A photon is emitted when an electron moves from a higher energy state to a lower energy state. The energy of the emitted photon is equal to the difference in energy between the energy levels in the transition.

• Each line of the emission spectrum corresponds to a different energy level transition within the atom
  • Electrons can transition between energy levels absorbing or emitting a discrete amount of energy
  • An excited electron can transition down to the next energy level or move to a further level closer to the ground state

• For example, if an atom has six energy levels:
  • At low temperatures, most electrons will occupy the ground state n = 1
  • At high temperatures, electrons may be excited to the most excited state n = 6

Energy and frequency of a photon are directly proportional

• The energy of a photon can be calculated using the formula:

• 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 (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

Difference in discrete energy levels

• The difference between two energy levels is equal to a specific photon energy
• The energy of the photon is given by:

• Where:
  • E₁ = energy of the lower level (J)
  • E₂ = energy of the higher level (J)

• Using the wave equation, the wavelength of the emitted, or absorbed, radiation can be related to the energy difference by the equation:

• This equation shows that:
  • The larger the difference in energy between two levels ΔE, the shorter the wavelength λ and vice versa