CHEM1011
Bold (green) – Week number and core focus
Italic (green) – Threshold or mastery content, heading
Italic and underlined (black) – Subheading
Week 1: Quantisation of energy
Threshold Content
Waves and particles
In classical mechanics, the motion of objects can be described as particles or waves.
- The properties of particles were described by Newton (Newtonian mechanics) and the properties of waves
by Maxwell (wave mechanics).
- In quantum mechanics, a single object like an electron or light can display both particle-like and wave-like
behaviour and thus we need a more complex model to describe their behaviour in systems.
Particles
- Classical particles are governed by Newton's equations of motion and described mathematically using
concepts such as momentum, energy, forces, torques, etc.
§ Classical particles have mass, but mass-less quantum mechanics objects can have particle-like
behaviour; e.g. a quantised packet of energy (photon) of light.
Observable properties of particles
- There are two main ways to tell if an object can be treated as a particle:
§ Weight it (this will only work for classical particles)
§ When two particles collide, they can change the speed of the other object by transferring
momentum (think two snooker balls hitting each other).
Classical waves
- Waves can carry energy through
different media, such as water waves,
sound waves, or vibrations of strings.
- There are three important properties
of waves you need to know:
§ Wavelength: The symbol,
lambda, the wavelength is the
distance between two wave
crests (or troughs). It has
dimensions of length; the SI
unit is meter, m.
§ Frequency: Given many
symbols, including f, and v
(Greek, nu). The frequency is
the number of waves that
pass a given point in each
second and therefore has
units of s⁻¹. This unit is also
called Hertz (Hz) after the German scientist, Heinrich Hertz, who was the first person to prove
conclusively the presence of electromagnetic waves.
§ Speed: Waves also propagate through a medium at a speed that depends on the medium. Speed, s,
is measured in m s⁻¹.
, - These three properties are related by the equation:
§ Speed = Frequency x Wavelength
Electromagnetic waves
- The waves that we are mostly
concerned with in chemistry
are electromagnetic (EM)
waves, or EM radiation.
- EM radiation includes light, X-
ray, etc. and has oscillating
electric and magnetic
fields at right angles to
each other, propagating as
waves through space.
- The speed of an EM wave
(e.g. light), c, is one of the fundamental constants of nature:
§ c = 2.998 x 10⁸ m s⁻¹
Observable properties of waves
- There are two ways to tell if an object is a wave:
§ Measure its wavelength or frequency directly
(best for classical waves)
§ Observe interference patterns.
- "Interference" is a term that means waves interact to
produce regions of high and low intensity.
- For sound waves, this is regions of loud and soft sound; in
water waves, regions of high waves and low waves.
- For waves of EM radiation (like light) this is regions of
brightness and darkness.
- For this course, know that waves interfere, including
diffraction.
Regions of the EM spectrum
- The EM spectrum can be broken into different regions, characterised by wavelength or frequency and
you are expected to recognise these regions by their names and key wavelengths and frequencies.
- Visible light constitutes a very small region of the EM spectrum, which we define as 380-780 nm.
- Ultraviolet light (10-380nm) excites electrons and can initiate chemical change.
- Absorption of infrared light (780nm-1mm) causes molecules to vibrate. IR light is usually
associated with heat.
,Wave-particle duality and the photoelectric effect
In the later stages of the 19th century, physicists began to find problems with the definitions of light as an
electromagnetic wave, and particles behaving as Newton described.
- Over the next 30 years, light was discovered to have some properties of particles, while small particles were shown to
behave like light.
§ This is known as wave-particle duality.
- Essentially, classical theories where light is considered just as a wave and electrons are considered just as a
particle are insufficient to describe all their experimental behaviour.
- A more complete theory is that of quantum mechanics, which is essential for understanding chemistry.
- There are two very important consequences of the wave-particle duality to chemistry.
1. Discretised photons of light exist with a specific amount of energy. A photon can be absorbed by or emitted by
atoms, molecules or surfaces which increase or decrease in energy; this is the basis of spectroscopy.
2. Electrons in atoms and molecules need to be considered not as point particles orbiting a nuclei but as
extended objects (orbitals or wavefunctions) with shape and quantised energy.
Experimental evidence that light behaves as a particle
- In 1900, Planck proposed that light could only be emitted in “quantised” form, i.e. discrete "packets" or
"quanta" of light, with the energy of each quantum depending on the frequency of the light.
- The energy of light at a particular frequency was therefore an integer number of packets (quanta), rather
than a continuous variable as in the classical description.
§ Using his theory of “energy quantum”, Planck was able to replicate the observed energy dependence
of emitted light.
- Planck thought that his "energy quanta" had no practical application. In 1905, Albert Einstein postulated that
this smallest quantum of light was real and comes in 'packets' or bundles that are localised (i.e. particle-light).
He called these 'light quanta', which later became known as photons.
- Einstein’s theory was able to explain several, then, unexplained experimental observations, including the
ultraviolet catastrophe and the heat capacity of solids.
§ The most famous breakthrough of all was explaining the “photoelectric effect” which had been
experimentally observed several years earlier.
Photon: A massless, chargeless particle with a discrete energy based on its frequency.
The photoelectric effect
- The photoelectric effect was first described by Heinrich Hertz in 1887.
§ He observed that shining light of a sufficiently high frequency onto the surface of a metal would
eject electrons.
§ He observed that light below a specific frequency would NOT release electrons (i.e a frequency
threshold), whereas all frequencies
higher than this threshold would.
§ He also observed that the frequency
threshold was different for
different metals.
- Classical physics was unsuccessful in explaining
this behaviour.
- According to classical physics, if the intensity
of the light was increased further and further
(turning up the brightness), then electrons
would eventually be released.
§ However, the experiments showed
that it was the frequency that was critical,
not the intensity.
, - Einstein’s theory of photons
explained the frequency
dependence.
- Einstein determined that the
energy of one photon of light was
proportional to its frequency, with
the same relationship as
proposed by Planck:
§ E = hf
• E = energy in
Joules
• f = frequency of light in Hertz (Hz)
• h = Planck’s constant: h = 6.626 x 10-34 J s
- This equation can be used in combination with the formula c = wavelength x frequency
- Using these two equations it is possible to calculate the energy, frequency and wavelength of a photon from
any one of these properties.
- Combining the equations:
§ E = hc / wavelength
§ E = hf
- The energy of a photon of light is proportional to its frequency.
- Hertz' experiment showed that there is a minimum energy a photon must have to release an electron from an
atom. For an electron bound in an atom we can refer to this as the binding energy.
- We can expect this energy to be different for different types of atoms.
- Under certain conditions this can be referred to as the ionisation energy of an electron in an atom.
Understanding atomic structure from the photoelectric effect
- If electrons are bound to a metal with a specific binding energy, then one photon with energy in excess of
this binding energy can liberate one electron.
- Moreover, the photon energy in excess of the binding energy was equal to the kinetic energy of the
released electron.
§ Typically, we define zero energy as that of the free electron with zero kinetic energy.
• Then the binding energy is a negative value, while the kinetic energy is a positive value.
- The reason for defining zero for an unbound or free electron is that this is the same value for every metal.
Each metal will then have a different (negative) binding energy.
§ See video on Moodle for further explanation on this.
- In essence, light has properties of particles, and particles have wave properties. The electron, in particular, displays
prominent characteristics of both particles and waves.
Quantisation of electron energies
We have developed the idea that light displays properties of particles (momentum, quantized energy, localised
position) and the particles display wave-like properties.
- We also discussed electrons as being the earliest and most important (for chemistry) example of a particle
with wave properties.
Standing waves
- When waves are confined they can
form “standing waves”.
- Standing waves occur for all wave types.
Standing waves – in one direction
- Waves in one direction: waves on a guitar string.
Bold (green) – Week number and core focus
Italic (green) – Threshold or mastery content, heading
Italic and underlined (black) – Subheading
Week 1: Quantisation of energy
Threshold Content
Waves and particles
In classical mechanics, the motion of objects can be described as particles or waves.
- The properties of particles were described by Newton (Newtonian mechanics) and the properties of waves
by Maxwell (wave mechanics).
- In quantum mechanics, a single object like an electron or light can display both particle-like and wave-like
behaviour and thus we need a more complex model to describe their behaviour in systems.
Particles
- Classical particles are governed by Newton's equations of motion and described mathematically using
concepts such as momentum, energy, forces, torques, etc.
§ Classical particles have mass, but mass-less quantum mechanics objects can have particle-like
behaviour; e.g. a quantised packet of energy (photon) of light.
Observable properties of particles
- There are two main ways to tell if an object can be treated as a particle:
§ Weight it (this will only work for classical particles)
§ When two particles collide, they can change the speed of the other object by transferring
momentum (think two snooker balls hitting each other).
Classical waves
- Waves can carry energy through
different media, such as water waves,
sound waves, or vibrations of strings.
- There are three important properties
of waves you need to know:
§ Wavelength: The symbol,
lambda, the wavelength is the
distance between two wave
crests (or troughs). It has
dimensions of length; the SI
unit is meter, m.
§ Frequency: Given many
symbols, including f, and v
(Greek, nu). The frequency is
the number of waves that
pass a given point in each
second and therefore has
units of s⁻¹. This unit is also
called Hertz (Hz) after the German scientist, Heinrich Hertz, who was the first person to prove
conclusively the presence of electromagnetic waves.
§ Speed: Waves also propagate through a medium at a speed that depends on the medium. Speed, s,
is measured in m s⁻¹.
, - These three properties are related by the equation:
§ Speed = Frequency x Wavelength
Electromagnetic waves
- The waves that we are mostly
concerned with in chemistry
are electromagnetic (EM)
waves, or EM radiation.
- EM radiation includes light, X-
ray, etc. and has oscillating
electric and magnetic
fields at right angles to
each other, propagating as
waves through space.
- The speed of an EM wave
(e.g. light), c, is one of the fundamental constants of nature:
§ c = 2.998 x 10⁸ m s⁻¹
Observable properties of waves
- There are two ways to tell if an object is a wave:
§ Measure its wavelength or frequency directly
(best for classical waves)
§ Observe interference patterns.
- "Interference" is a term that means waves interact to
produce regions of high and low intensity.
- For sound waves, this is regions of loud and soft sound; in
water waves, regions of high waves and low waves.
- For waves of EM radiation (like light) this is regions of
brightness and darkness.
- For this course, know that waves interfere, including
diffraction.
Regions of the EM spectrum
- The EM spectrum can be broken into different regions, characterised by wavelength or frequency and
you are expected to recognise these regions by their names and key wavelengths and frequencies.
- Visible light constitutes a very small region of the EM spectrum, which we define as 380-780 nm.
- Ultraviolet light (10-380nm) excites electrons and can initiate chemical change.
- Absorption of infrared light (780nm-1mm) causes molecules to vibrate. IR light is usually
associated with heat.
,Wave-particle duality and the photoelectric effect
In the later stages of the 19th century, physicists began to find problems with the definitions of light as an
electromagnetic wave, and particles behaving as Newton described.
- Over the next 30 years, light was discovered to have some properties of particles, while small particles were shown to
behave like light.
§ This is known as wave-particle duality.
- Essentially, classical theories where light is considered just as a wave and electrons are considered just as a
particle are insufficient to describe all their experimental behaviour.
- A more complete theory is that of quantum mechanics, which is essential for understanding chemistry.
- There are two very important consequences of the wave-particle duality to chemistry.
1. Discretised photons of light exist with a specific amount of energy. A photon can be absorbed by or emitted by
atoms, molecules or surfaces which increase or decrease in energy; this is the basis of spectroscopy.
2. Electrons in atoms and molecules need to be considered not as point particles orbiting a nuclei but as
extended objects (orbitals or wavefunctions) with shape and quantised energy.
Experimental evidence that light behaves as a particle
- In 1900, Planck proposed that light could only be emitted in “quantised” form, i.e. discrete "packets" or
"quanta" of light, with the energy of each quantum depending on the frequency of the light.
- The energy of light at a particular frequency was therefore an integer number of packets (quanta), rather
than a continuous variable as in the classical description.
§ Using his theory of “energy quantum”, Planck was able to replicate the observed energy dependence
of emitted light.
- Planck thought that his "energy quanta" had no practical application. In 1905, Albert Einstein postulated that
this smallest quantum of light was real and comes in 'packets' or bundles that are localised (i.e. particle-light).
He called these 'light quanta', which later became known as photons.
- Einstein’s theory was able to explain several, then, unexplained experimental observations, including the
ultraviolet catastrophe and the heat capacity of solids.
§ The most famous breakthrough of all was explaining the “photoelectric effect” which had been
experimentally observed several years earlier.
Photon: A massless, chargeless particle with a discrete energy based on its frequency.
The photoelectric effect
- The photoelectric effect was first described by Heinrich Hertz in 1887.
§ He observed that shining light of a sufficiently high frequency onto the surface of a metal would
eject electrons.
§ He observed that light below a specific frequency would NOT release electrons (i.e a frequency
threshold), whereas all frequencies
higher than this threshold would.
§ He also observed that the frequency
threshold was different for
different metals.
- Classical physics was unsuccessful in explaining
this behaviour.
- According to classical physics, if the intensity
of the light was increased further and further
(turning up the brightness), then electrons
would eventually be released.
§ However, the experiments showed
that it was the frequency that was critical,
not the intensity.
, - Einstein’s theory of photons
explained the frequency
dependence.
- Einstein determined that the
energy of one photon of light was
proportional to its frequency, with
the same relationship as
proposed by Planck:
§ E = hf
• E = energy in
Joules
• f = frequency of light in Hertz (Hz)
• h = Planck’s constant: h = 6.626 x 10-34 J s
- This equation can be used in combination with the formula c = wavelength x frequency
- Using these two equations it is possible to calculate the energy, frequency and wavelength of a photon from
any one of these properties.
- Combining the equations:
§ E = hc / wavelength
§ E = hf
- The energy of a photon of light is proportional to its frequency.
- Hertz' experiment showed that there is a minimum energy a photon must have to release an electron from an
atom. For an electron bound in an atom we can refer to this as the binding energy.
- We can expect this energy to be different for different types of atoms.
- Under certain conditions this can be referred to as the ionisation energy of an electron in an atom.
Understanding atomic structure from the photoelectric effect
- If electrons are bound to a metal with a specific binding energy, then one photon with energy in excess of
this binding energy can liberate one electron.
- Moreover, the photon energy in excess of the binding energy was equal to the kinetic energy of the
released electron.
§ Typically, we define zero energy as that of the free electron with zero kinetic energy.
• Then the binding energy is a negative value, while the kinetic energy is a positive value.
- The reason for defining zero for an unbound or free electron is that this is the same value for every metal.
Each metal will then have a different (negative) binding energy.
§ See video on Moodle for further explanation on this.
- In essence, light has properties of particles, and particles have wave properties. The electron, in particular, displays
prominent characteristics of both particles and waves.
Quantisation of electron energies
We have developed the idea that light displays properties of particles (momentum, quantized energy, localised
position) and the particles display wave-like properties.
- We also discussed electrons as being the earliest and most important (for chemistry) example of a particle
with wave properties.
Standing waves
- When waves are confined they can
form “standing waves”.
- Standing waves occur for all wave types.
Standing waves – in one direction
- Waves in one direction: waves on a guitar string.
