Electrons and Energy Levels

1. Photons

• A photon is the name given to a discrete packet (quantum) of electromagnetic energy. It is the
  fundamental particle of light and all other forms of electromagnetic radiation, carrying
  energy proportional to the radiation frequency but having zero rest mass.
• Photons exhibit both wave-like and particle-like properties, a concept known as
  Wave-Particle Duality.
• For example, an X-ray photon can have a wavelength of 1nm and frequency of 3 × 1017Hz,
  and a photon of yellow light has a wavelength of 600nm and frequency of 5 × 1014Hz.
  The energy carried by a photon is discussed below.

1.1 Energy of photons

The energy of a photon can be calculated using the equation:
E=hf

• E is the energy of the photon,
• h is Planck’s constant (6.63×10−34Js),
• f is the frequency of the electromagnetic wave

1.2 Intensity

Dependence

• Energy carried by photons
• Number of photons
• Area

• Intensity increases:
  When the light source is made more powerful, so more photons are transferred per
  second; for example, the intensity of light from a 100 W bulb is greater than the
  intensity from a 10 W bulb if all other factors remain the same
• When each photon transfers more energy; for example, a beam of ultraviolet photons is
  more powerful than a beam transferring the same number of infrared photons per second
• When the light is incident on a smaller area; for example, when you move closer to a
  light source, more light energy enters your eye each second, and you sense a greater
  intensity of light.
• Intensity follows an inverse square law, so the intensity of light measured from a light
  source quadruple if you half the distance away from the same light source.

1.3 The Electron Volt

• An electron volt (eV) is a unit of energy commonly used in atomic and nuclear physics.
• It is defined as the amount of kinetic energy gained or lost by an electron when it is
  accelerated through an electric potential difference of one volt.
• An electron volt (eV) is a unit of energy equal to 1.6 × 10−19 J. It is the energy gained by an
  electron when it is accelerated through a potential difference of 1 volt.
• The work done in electron volts is calculated using:

• Where: W is the energy transferred in electron volts
• V is the potential difference in volts
• Q is the electron charge, 1.6 × 10−19C.
• To convert joules to electron volts, divide the energy in joules by 1.6 × 10⁻¹⁹J/eV
• To convert electron volts to joules, multiply the energy in electron volts by 1.6 ×10⁻¹⁹J/eV

1.4 Absorbing and emitting photons

• An electron in an atom gains and loses energy as it moves within the atom.
• The electron has a combination of kinetic energy and electrostatic potential energy.
• The electron moves further from the nucleus if it gains the right amount of energy by absorbing
  a photon. We say the electron moves to a higher energy level.
• If the electron drops from a higher energy level to a lower energy level, it loses its surplus
  energy by emitting a photon and moving closer to the nucleus.

1.5 Quantized energy levels

Examples:

• You come across this idea when you use stairs. You cannot climb part of a step, but must
  gain or lose gravitational potential energy in precise amounts that match the energy difference
  between each stair.
• You can gain or lose energy in larger amounts to move between stairs further apart, but
  you are still only allowed fixed values of energy. However, while stairs all have the same
  spacing, the arrangement of energy levels in atoms is more complicated.

2. Excitation and Ionization

• Excitation occurs when an atom gains or loses an electron and becomes charged. It has
  been ionized.
• Ionization is the energy required to remove an electron from its ground state to infinity, i.e.
  to become detached from the atom.
• Ground State: When electrons in an atom are in their lowest energy state.
• Excited State: When an electron in an atom moves to a higher energy level (above the
  ground state) after it has absorbed energy, Excitation occurs.

2.1 Line spectra and continuous spectra

• Diffraction Grating: A diffraction grating is a piece of transparent material ruled with very
  closely spaced lines, used to see the diffraction of light.
• This is made from a transparent material with many gaps between very closely ruled lines, or
  ridges.
• Light passing between each gap in the grating spreads and interferes with light spreading
  through neighbouring lines.
• This process splits the light into a spectrum of the colours it contains
• Continuous Spectrum: A continuous spectrum is a spectrum where all frequencies of
  radiation or colours of light are possible.
• Sunlight and light from a filament bulb give a continuous spread of colours that merge into each
  other. This is a continuous spectrum.
• Line Spectrum: A line spectrum is a spectrum of discrete coloured lines of light.
• The pattern of lines is characteristic for certain elements.
• All fluorescent bulbs have a similar line spectrum because electrons in the mercury vapors inside
  them have the same excited states regardless of the shape of the bulb.

2.2 Emission Spectra

An emission spectrum is the spectrum of light emitted by a substance that has absorbed energy.
When the electrons in an atom or molecule absorb energy, they move to higher energy levels.

• As they return to their original energy levels, they emit photons of specific wavelengths, creating
  a spectrum of discrete lines.

Example:

• The light emitted by excited hydrogen gas
• When you heat salts in a Bunsen flame, sometimes you see different colours. For example,
  compounds with copper in them emit green light, and sodium compounds a bright yellow light.
  These colours are determined by electrons falling from one energy level to another, emitting the
  particular colour of light specific to that element.

2.3 EAbsorption Spectra

Absorption spectra are a spectrum of dark lines seen on a colored background produced when a
gas absorbs photons.

• An absorption spectrum can be seen when light shines through a gas, and electrons in the atoms
  absorb photons corresponding to the possible energy transitions
• All other photons pass through, as they cannot be absorbed.
• The dark lines of the spectrum correspond to the wavelengths of the possible energy transitions
  for the electrons of the gas atoms.
• The electrons become excited, moving from lower energy levels to higher energy levels.
• In fact, the electrons then fall back to their original energy state, releasing photons as they do so,
  but the spectrum still appears to have black lines as these photons are emitted in all directions.

2.4 The Energy of Spectral Lines

E2 − E1 = hf

Where

• E1 and E2 are the energies of energy levels 1 and 2 (in J),
•  h is the Planck constant (in Js)
• and f is the frequency of radiation (in Hz).

Many spectral line diagrams show the energy in electron volts. One electron volt is 1.6 × 10−19 J
Figure shows energy levels in a hydrogen atom.

• The ground state is labeled as n = 1, and the first excited energy level is n = 2 and so on.
• The ionisation energy is 13.6eV (moving the electron from its ground state up to n = ∞). The
  arrows indicate the electron moves to a lower energy level, emitting photons.
• An emission spectrum would be seen.
• The energy is always negative as we define the zero point of energy is when the electron is at
  infinity. This energy gets lower as the electron gets closer to the nucleus.
• The energy of the green line is the difference in energy between n = 4 and n = 2, that is −0.85eV
  − (−3.41eV), or 2.56eV.
• 2.56eV is equivalent to 4.1 × 10⁻¹⁹ J.

3.  The Fluorescent Tube

1) A fluorescent tube is a glass tube filled with mercury vapour and coated inside with fluorescent materials called phosphors.
2) When the light is switched on, the cathode is heated causing thermionic emission.
3) Thermionic emission occurs when a heated cathode releases free electrons from its surface. The free electrons have a range of energies.
4) A potential difference of 500V, applied across ends of the glass tube, accelerates the electrons from the cathode to the anode through the mercury vapor.
5) If the free electrons collide with mercury atoms inelastically, some energy may be transferred from the free electrons to the mercury atoms.
6) These atoms may be ionised or excited, provided the free electrons transfer enough kinetic energy.
7) High-energy electrons cause ionisation, and lower energy electrons cause excitation.
8) As the mercury atoms in the vapour become ionised (lose electrons), a mixture of ions and free electrons is created; this is called a plasma.
9) When the electrons in the excited mercury atoms return to their ground state, they release photons of ultraviolet radiation.
10) These photons strike the phospors in the coating and are absorbed. The energy is re-emitted as visible light, and some energy is transferred as heat.