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Chemistry Revision

 » Isotopes

• They are atoms of the same elements which have the same number of protons in their atomic nuclei but differing numbers of neutrons.
• A certain isotope can be expressed by its atomic symbols
• Nucleons: anything inside the nucleus

 

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Properties of the Nucleus

 » Introduction

• Einstein’s discovery of energy mass equivalence led to humans harnessing large amounts of energy with an atom.
• Combustion reactions were used before we were able to harness energy. These were associated with fossil fuels. Nuclear reactions allow us to harness the abundant naturally occurring radioactive substances.

※ Industrial & medicinal applications

 » The Strong Nuclear Force

• Properties:

• Experiences by all Nucleons (Protons & Neutrons).
• Attractive over short ranges (≈ 1 femtometre – x 10^-15m)
• Strong enough to overcome electrostatic repulsion forces.
• Becomes repulsive at even closer distances.

                        

                    

 » Zone of Nuclear Stability

• This graph shows the criteria necessary to create a stable nucleus.
• The two factors that contribute to the nucleus’s stability is:

※ The Neutron – Proton Ratio

※ The total number of nucleus

                   

 » Properties of Radiation

• Alpha

※  Helium nucleus consisting of two protons & neutrons.

※ Often emitted to reduce mass of a radioactive substance.

     

• Beta

※ Fast moving electrons.

※ Often emitted to increase the stability of a radioactive substance.

• Gamma

※ Uncharged high energy & frequency electromagnetic radiation.

※ Often emitted to reduce the energy of a radioactive substance.

     

   

 » Radioisotopes

• Radioisotope: An unstable isotope will emit particles &/or radiation until it becomes stable.

                

• Every atom of the same element has the same number of protons. However, they can have different amounts of neutrons (therefore a different overall mass).
• Different isotopes have different configurations. Some isotopes (like Carbon-12) are stable whilst others (Carbon-14) are unstable/radioactive.

 » Nuclear Transmutations (Radioactive Decay)

• Nuclear Transmutation: the conversion of one chemical element to another through the emission of alpha or beta particles from the nucleus.
• Nuclear equations are used to demonstrate nuclear transmutations.
• There are other methods in which a nuclear can transmutate. These are Fission & Fusion.

       

 » Half-life in Radioactive Decay

• Half-life (t_^1/2): time taken for half the radioactive substance to decay.
• Different radioactive isotopes decay at different rates

• Examples:

※  Uranium-238: 4.5 x 10⁹ yrs.

※  Polonium-218: 1.4 x 10^-4 secs

• Implications of varying half-lives:

• Uranium’s long half-life makes it a dangerous isotope as it remains for a long period of time, whilst Polonium does not linger around long enough for it to be a useful isotope (for medical & industrial uses).
• Ideally, for diagnosis imaging, isotopes with half-lives between minutes & hrs are selected to minimise exposure whilst existing for long enough to serve its purpose
• Examples: Tc-99m to investigate bone function, bone disease & 1- 123 to assess thyroid function.

 » Radioactive Decay Equation

• The rate of decay of a certain number of atoms is proportional to the number of atoms present:

                

 • Process of Nuclear Fission:

• A neutron strikes the nucleus of a heavy & unstable isotope.
• The nucleus becomes unstable.
• Causing it to vibrate then split.

 • Process of Nuclear Fission:

• Two or three neutrons.
• Two smaller, lighter atoms.
• Heat energy.

  • Fermi’s Observation

• The advantages of neutron bombardment are:
• Enrico Fermi discovered that new radioactive elements could be produced when a target nucleus is struck by neutrons.
• •  Neutrons (due to zero change) are not deflected by the nucleus nor affected (repelled/attracted) by the electron clouds → worked better than charged particles..
  •  Slow neutrons can enter & interact with even the most massive, highly charged nucleus.
•  Fermi was successful between 1934-1938.
• However, when applied to Uranium, Fermi & his team found that rather than creating a single heavier isotope, several different isotopes were produced with different measurable half-lives.
• This was Fermi’s first observation of fission, although he couldn’t comprehend the nature of the process.
• In 1939, two Australian Physicists, Lise Meitner & Otto Frisch explained the process with bombardment. The Uranium nucleus broke down into two nuclei of roughly equal size. They named this process ‘nuclear fission’.

           

• Three neutrons are produced but only one neutron is required for nucleus fission so there was a possibility of a chain reaction.

 » Chain Reactions

• Nuclear Chain Reactions: a series of nucleus fissions imitated by a neutron produced in a preceding fission.

               

 » Controlled Chain Reactions

• Controlled Chain Reaction: a self-propagating nuclear reaction in which only one neutron released by the splitting of a nucleus is allowed to hit another nucleus to cause further fission resulting in the steady release of energy.
• The reaction will continue at a constant rate.
• Occurs in nuclear reactors & powerplants.

 » Uncontrolled Chain Reactions

• Uncontrolled Chain Reaction: a self-propagating nuclear reaction in which more than one neutron released by the splitting of a nucleus is allows to hit another nucleus to cause further fission resulting in energy being released exponentially.
• The reaction will continue at an increasing rate.
• Occurs in nuclear bombs or atomic bombs.

 » Nuclear Fusion

• Nuclear Fusion: the process in which two or more small nuclei combine to form a larger nucleus with the release of a large amount of energy (more energy released compared to nuclear fission).

 » Mass Defect & Binding Energy

• Mass Defect: the difference between the mass of the constituent nucleons & the mass of the nucleus.
• In order to separate the atoms into its constituent nucleons (i.e. break atoms apart), work needs to be done which means energy is required.
• Binding Energy: the energy needed is equal to the energy that holds the atom together in the first place.
• The mass of the nucleus is less than the mass of the nucleons (which make up the nucleus). This mass defect is related to binding energy.

• This explained by:

• Einstein’s relationship E = mc² . Mass & energy are equivalent.
• The Law of Conservation of Energy: cannot be created nor destroyed. It can only be converted from one form into another.
• Hence, the mass defect (missing mass) accounts for the energy that is gained (i.e. binding energy).

 » Binding Energy Per Nucleon

• Binding Energy of a Nucleus: the energy required to completely separate a nucleus into nucleons. Therefore, the binding energy is a measure of the stability of a nucleus.
• Iron is the most stable of all nuclei because it has the greatest binding energy per nucleon.
• Small nuclei, to the left, can make themselves more stable by clumping together into bigger nuclei (i.e. fusion).
• Large nuclei, to the right of iron, can make themselves more stable by splitting into smaller ones (i.e. fission).

                      

 » Energy in Nuclear Reactions

•  Different nuclei contain different numbers of protons & neutrons which means they possess different amounts of binding energy.
• Hence, during a nuclear reaction when an atom changes from one to another, energy can be released.
• • In nuclear fission, large unstable nuclei are split into smaller, more stable nuclei & binding energy is released.
  • In nuclear fusion, small unstable nuclei are joined together to form larger, more stable atoms & binding energy is released.

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The Origins of the Elements

 » Introduction

• The universe includes all of space & time & its contents (including planets, stars, galaxies & other forms of space & matter).
• Humans have always questioned the finite or infinite nature of the universe, what came before the universe, what will come after the universe & other questions we still don’t understand. 

 » Theories of the Universe

• Many astronomers have wondered about the origin of the universe. Many attempts have been made throughout hundreds of years to try and explain how our universe came to begin & what it looks like now.
• Early on, the universe was thought to consist of our solar system & the stars. Today it is understood that our solar system is just one of many in our galaxy, & that our galaxy (The Milky Way) is just one of many.
• The size & scale of the universe is so large that it is nearly incomprehensible.
• If the Earth was represented by a golf ball, the Sun would be length of a sedan, & Star Arcturus would be the length of a football field.

   

• 16th Century BC: Mesopotamian culture believed the Earth to be a flat disc sitting on a ‘cosmic ocean’.
• 4 th Century BC: Aristotle proposed a universe with the Earth at the centre (Geocentric model).
• 1543: Nicolaus Copernicus publishes his Sun centred model of the universe. It would take over 100 years for evidence to be gathered proving his idea.
• 1584: Giordano Bruno proposed a model where the Copernican solar system is not the centre of the universe, arguing it is one of many star systems.
• 1687: Sir Isaac Newton creates laws to explain gravity, describing how objects orbit & move throughout the universe. He also proposes that the universe is static in size.
• 1915: Albert Einstein published his theories on relativity, linking space & time in the universe. He also believes that the universe is static in size.
• 1922: Alexander Friedmann proposes an expanding model of the universe.
• 1923: Edwin Hubble discovered an object that sits outside of our Milky Way galaxy. This implied that the Milky Way is one of many galaxies.
• 1929: Edwin Hubble builds on his discovery, using the Doppler Effect to show that the universe is expanding.
• 1948: George Gamow builds on Hubble’s experiment, proposing the ideas which would lead to the Bing Bang Theory.

 » The Expanding Universe

• In 1924, Hubble was studying a group of stars in a nebula (a gas from which a star is formed) called Andromeda.
• He calculated the distance of Andromeda to be 800,000 light years away.
• This distance greatly exceeded the distance of any known star at the time as well the length of the Milky Way (approx. 100,000 light years).
• Hubble’s work suggested evidence that the stars in Andromeda existed in a separate galaxy.
• The implication if that there must exist other galaxies in the universe apart from our Milky Way.
• Five years later, Hubble used spectrology from Andromeda Nebula (now known as the Andromeda galaxy) as evidence for the expansion of the universe.
• Recall that the Doppler Effect occurs due to the relative motion of the source of a wave & the observer. If the wave is light, the Doppler Effect is explained as a redshift of blueshift of spectral lines.
• Hubble observed that the spectral lines were redshifted. This showed that Andromeda was moving away from us. When he observed other objects outside of our galaxy, he found a similar result.
• This gave evidence to an expanding universe.

 » Hubble’s Law

• Hubble’s law describes the rate at which distant galaxies are moving away from us

• A parsec is a unit of distance in Astrophysics (study of astronomy related to Physics). It is equal to 3.2616 light years (ly), 206265 Astronomic units (AU) & 3.086 x 10¹⁶ metres (m).
• Hubble’s law implies that the universe is expanding at an increasing rate.

                                   

•  Balloons's Analogy:

• The surface of the balloon represents all of space.
• As air fills the balloon the surface of the balloon expands.
• If stickers on the balloon are used to represent the galaxies/star systems, it can be seen that the stickers don’t get bigger.
• So, whilst the space between the galaxies expand, the actual objects in space don’t get larger.

 » The Big Bang

• 1930: Physicists agreed that the universe is not static & keeps expanding.
• They concluded that the universe must have started out tiny from one point.
• 1940: George Gamow proposed the Big Band Theory.

            

 » The Singularity

• The universe is thought to have begun with a single point tiny point of energy. It had extremely high temperature, density & pressure. Space, matter, & time didn’t exist & neither did the laws of physics.
• The universe expanded from a single point, releasing immense amounts of energy that cooled.
• The singularity occurred roughly 13.8 billion years ago. However, from zero to approximately 10^-43 seconds, there is little understanding about how the universe looked to be.

 » Inflation & Energy Dominant Period

• From 10^-36 seconds to 10^-32 seconds, the universe underwent extremely rapid exponential expansion, known as inflation.
• The universe expanded from that single point (growing 10²⁶ time larger) to the size of around 10 cm, releasing immense amounts of energy.
• At this point the universe is still over 10 billion degrees hot, this prevents any particles from forming. As the universe continues to expand, it cools.
• As it cooled, energy was transformed into matter (discovered by Einstein).
• At 10^-9 seconds, the universe stretched to a billion km in diameter. It is now cool enough for fundamental particles to exist in a stable state.

                     

 » Recombination

• Initially, some energy was transformed into fundamental particles of matter:

※  Electrons

※  Quarks (building blocks of protons & neutrons)

                                             

• After a few minutes, quarks combined to form protons & neutrons. This process is called recombination.
• Hundreds of thousands of years later, the universe cooled sufficiently for electrons, protons & neutrons to combine & form atoms.
• The energy released was not uniform. Some areas had much higher density of energy. Places with more energy had more energy to work with to make protons and neutrons to build, which would eventually create planets.

 » Radiation Release

• At this point, a large amount of radiation released from the Big Bang was freed & cooled down. This radiation still exists today.
• This is called Cosmic Background Radiation & exists as a microwave signature.
• It was predicted by Gamow in 1948 & later discovered in 1964.

                                 

 » Accretion

• As the universe was expanding & cooling, particles lost kinetic energy & began to attract each other through gravity. This formed regions of high mass & density.
• This region then began to attract other nearby materials & gain mass. This process is called accretion.
• Due to accretion, matter in the universe formed discrete gas clouds known as protogalaxies.
• As further accretion occurred, galaxies were formed.
• Accretion continued to happen inside galaxies to form stars (i.e. our Sun is formed in the Milky Way).
• To this day, our universe continues to expand (13.8 billion years later).

 » Cosmic Background Radiation

• In the early state of the universe, the temperature was so high that atoms didn’t exist.
• The universe consisted of radiation & elementary particles. The radiation was trapped, travelling short distances before being scattered by electrons. As a result, the universe was opaque.
• As the universe cooled to 3000K; 380,000 years later, atoms were able to be formed. Free electrons were no longer present to scatter the radiation.
• The universe become transparent as the radiation was now able to disperse freely in the universe.

 » Stars

• Star: a type of astronomical object consisting of a luminous spheroid of plasma (dense, ionised gas) held together by its own gravity.
• It wasn’t until the time of Galileo & Newton, when scientists began to understand that stars were sun-like objects.
• Astronomers now understand how stars form, the reactions that take place in the star & the significant role that stars play in forming the universe.
• Except for those created by the Big Bang, every element was synthesised inside a star.
• Different methods (including spectrology) yield information into the nature of stars (even if they are millions of light years away from Earth).

 » Lifestyle of a Star

                

• All stars begin as large gas clouds (mainly hydrogen) called nebulas. A single nebula might be the birthplace of thousands of stars.
• If the gas is sufficiently cooled, the particles in the cloud will begin to clump due to gravitational acceleration.
• This process starts slowly but speeds up as the cloud becomes denser.
• The cloud now consists of 2 parts: A rapidly contracting core & the slower contracting surroundings.
• As the cloud continues to contract, its temperature increases. The GPE (which caused the cloud to contract) changes into thermal energy.
• This heat creates an outwards pressure that works against gravity, but only slightly.
• As the core gets denser & hotter it stabilises. At this point, fusions haven’t occurred yet & the body is called a protostar.
• This process occurs over one million years.

                                       

• Eventually the core may reach a sufficient temperature to trigger the nuclear fusion of hydrogen to helium which settles to the centre (helium is denser). The hydrogen moves to the shell around the helium core.
• Once nuclear fusion of hydrogen begins, the star is officially a main sequence star.

  

• Hydrostatic equilibrium helps a main sequence star remain a stable size.
• If the star is at equilibrium the inwards pressure (due to gravity) is balanced by the outwards pressure (due to nuclear reactions).
• The hydrogen supply in the core will dwindle over time & the core will begin to collapse under gravity.

                                   

• If the mass of the star > 0.3 M_o, the gravitational collapse increases the temperature & helium fusion is triggered at the core. This forms a red giant.
• If the mass of the star > 0.3 M_o, the gravitational collapse increases the temperature & helium fusion is triggered at the core. This forms a red giant.
• Red Giant Star: characterised by the nuclear fusion of helium at the core. The remaining hydrogen fusion occurs in the outer shell.
• Eventually red-giants will begin to run out of helium, & the star contracts due to gravitational forces (it’s no longer at hydrostatic equilibrium).
• If the red giant is large enough (super red giant), the core will heat up to a sufficient temperature to create heavier elements from carbon to iron.
• Once a star is no longer able to fuse elements, it will begin to die. The path it takes again will dependent on its size.
• If the mass of the red giant is < 0.5 M_o, it will run out of helium & collapse. A nova will occur where the star will release energy, gently shed its outer layers of gas.
• This is called a planetary nebula. Whatever energy isn’t shed forms a white dwarf.

       

• If the mass of a red giant > 0.5 M_o, a supernova explosion will occur, releasing a giant amount of energy.

•  The mass of the core will then determine its corpse:

• m < 1.4 M_o: the core becomes a white dwarf which eventually a black dwarf
• 1.4 M_o < m < 3 M_o: gravity will be sufficient to collapse electrons into protons forming a neutron star.
• m > 3 M_o: the neutrons formed by the collapse of protons & electrons will collapse further to form a black hole.

  

• White Dwarf: a collapsed star with no more nuclear fusion reactions as a source of energy.
• It will gradually radiate its energy & cool down.
• As it continues to radiate its energy over time, its temperature will decrease.

                

• When it no longer emits any heat or light, it is then known as a black dwarf.

 » Star Surface Temperature

• A star’s surface temperature is linked to the radiation produced by the star in a process called black body radiation.
• Recall that the peak wavelength of a heated object corresponds to the surface temperature & the colour of the star.

                      

                

 » Star Luminosity

• Luminosity: the energy radiated by an object per second.
• The luminosity of our sun is 3.83 x 10²⁶ W (L_o).

                       

• Brightness: the energy received per square metre per second.

         

 » Hertzsprung – Russel Diagram

• A Hertzsprung – Russel diagram is a graph of a star’s luminosity against its colour/surface temperature.
• 1920: Ejnar Hertzsprung & Henry Russel independently discovered that plotting the luminosity of stars against their surface temperature resulted in different groupings of stars with different characteristics.

 

• This diagram allows astronomers to classify stars & understand its evolution.

※  Main Sequence Stars:

• It becomes more luminous & massive when moving from bottom right to top left. The source of energy is the nuclear fusion of hydrogen at the core of the stars.

※  Red Giants:

• Extraordinarily large in size
• Nuclear fusion of helium occurs at the core of the stars.

※  White Dwarfs:

• No nuclear fusion.
• Collapsed star corpses.

                                        

 » Mass Energy Equivalence

• Originally astronomers hypothesised that chemical reactions inside the sun, generating heat & light which then travelled to Earth.
• However, based on the mass & energy output of the Sun this was ruled out.
• In order for chemical reactions (between the Sun’s atoms) to be the source of the radiation, the Sun would need a hundred million times more atoms.
• Chemical reactions could therefore not be the driving force behind a star’s energy output.
• Einstein is the first scientists to theorise the relationship between mass & energy, which would help explain how the Sun is able to generate massive amounts of energy.
• Einstein’s famous equation was published in 1905 & identifies that anything with mass has an equivalent amount of energy.

                 

• From examples, we can see that due to the c² factor, even a small amount of mass has a large associated amount of energy.
• Mass can be converted to energy through chemical reactions, nuclear reactions & other forms of energy transfer
• It was believed that Stars (like the Sun) utilised this property to produce the EMR it released.

                                  

                                     

• In main sequence stars helium is formed from hydrogen in one of two ways:

※ The proton-proton chain reaction (PP).

※  The carbon-nitrogen-oxygen cycle reaction (CNO).

• The PP chain reaction occurs mainly in smaller main sequence stars (stars less than 1.3M_o). It changes 4H atoms to 1He atom.
• This process occurs in three main steps:

                   

                           

           

• The CNO cycle involves six steps:

                        

                           

       

 » Other Measurements of Stars

• Parallax is a way of measuring the distances between objects in space.
• It relies on a phenomenon known as Parallax Shift.

       

• Parallax Shift: the difference in the position of an object (against a background) due to different viewing angles.
• Early on, astronomers couldn’t detect the parallax shift of stars in the sky (this was one of the key arguments used to justify that the Earth was stationary).

                                     

                                    

• When better telescopes were developed in the 19th century, it was seeing that the background stars moved very slightly over the period of one year.
• Astronomers concluded that the Earth was rotating around the Sun (& this creates the parallax).
• The parallax of an object can be used to approximate the distance to an object using the formula.

         

• The chemical composition of a star is discoverable using spectroscopy.
• Recall that an absorption spectrum is created by light passing through cool gases.
• Spectra lines are created by Earth’s atmosphere absorbing certain bands of light.
• Spectra lines are also created by the elements in the cooler regions of the stars (the outer layers). Studying these spectral lines will give us clues as to the chemical composition of the stars.

                           

※  In summary, for the elements found in the universe today:

• The lightest elements (hydrogen, helium, lithium, beryllium) began to form during the early stages of the Big Bang.
• Nuclear fusion inside main sequence stars created more amounts of helium, whilst the reactions inside the larger giant stars created medium sized elements (The elements of carbon up to iron). White dwarves did not undergo nuclear fusion.
• Supernova released enough energy to generate heavy elements all the way up to Uranium.

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The Structure of the Atom

 » Introduction

• Whilst physicists are interested by the very large objects in the universe, there is also a need to understand the smallest building blocks of matter as well.
• For most purposes, we can say that an atom is the smallest unit of ordinary matter that we can use to explain the properties of chemical elements.
• However, the atom itself is made up of smaller elementary particles; the proton, neutron & electron. These elementary particles were not discovered at the same time.

                                       

 » Dalton’s Atomic Model

• In 1803, an English chemist, John Dalton, proposed an atomic theory.

※  The basic postulates of Dalton’s atomic theory were as follow:

• Matter is composed of neutral, structure less & indivisible atoms
• The atoms of one element are identical
• Atoms of different elements have different atomic masses.
• Atoms are neither created nor destroyed in chemical reactions.
• Chemical reactions consist of combining, separating or rearranging atoms in simple whole number ratio.

 » Cathode Rays & The Electron

• By the 1850’s much was known about electricity & the conductor/insulator properties of materials. However, the fundamental nature of electricity was not yet understood.
• During this period of time, physicists we studying a device known as a cathode ray tube (or discharge tube).
• A cathode ray tube is a vacuum glass tube which has a very low pressure. Metal plates (called an anode & a cathode) are placed inside the tube & connected to a high voltage supply.

                           

• When the voltage supply is turned on, physicist saw that a current was flowing & that the glass glowed on the anode side of the glass. (Diagram is a vacuum tube)
• When a fluorescent screen was placed inside the tube a green stream/ray could be clearly observed. This was called a cathode ray.
• Scientist began experimenting with these tubes, demonstrating a number of important facts related to the properties of cathode rays.

  

 

 » J.J. Thomson’s Experiment

• Joseph John Thomson was the first physicist to demonstrate that an electric field could deflect the cathode rays. To do this, he built an almost perfect vacuum tube & applied an electric field.
• He successfully showed that the ray deflected towards the positive plate. This proved that the particles made up the cathode rays had a negative charge.
• By this time, the name electron was beginning to be used to describe the particles that made up the cathode rays.
• J.J. Thomson then set out the measure the mass of these particles

 » Thomson’s experiment involved two stages:

• By varying a magnetic & electric field, the forces would cancel out & leave the cathode ray un-deflected. This allowed for the velocity of the charge to be calculated.

           

• The electric field was then removed such that the cathode ray was deflected. The radius of curvature was then used to derive a charge to mass ratio.

        

• Whilst Thomson wasn’t able to measure the mass of the charges, he was able to measure the mass to charge ratio.

 » The Oil Drop Experiment

• In 1909 Robert Millikan created a device to measure the charge of an electron. This would then allow for the mass of the electron to be determined too.
• The apparatus built by Millikan involved an atomiser which sprayed a fine mist of oil into Region A.
• An electric field was set up in Region B, over tie some oil drops floated into this area, where it was then struck by an x-ray source. This caused the drops to become charged.

                              

                                     

• Therefore, Millikan could determine the charge of each oil droplet. After repeating the experiment multiple times, Millikan found that the charge of each oil drop was always a multiple of a small value
• This value was 1.6 x 10^-19 C, which was found to be the charge of an electron. Combined with Thomson’s experiment, the mass of an electron was calculated as 9.109 x 10^-31kg.

 » Thomson Atomic Model

• Although the mass of an electron was calculated as 9.109 x 10^-31 kg at the time the mass of an atom was already calculated to be 1.673 x 10^-27 kg.
• This meant that Dalton’s model of the atom was incomplete; there was a smaller particle inside of an atom.
• Thomson believed that the atom was still neutrally charged, so he proposed a ‘Plum Pudding Model’.
• “An atom is a positive sphere in which electrons are embedded”.

                                     

 » Rutherford Atomic Model

• Rutherford is a New Zealand physicist who is well known for his work with Alpha particle radiation.
• Alpha particles are a type of radiation that was known to come from radioactive elements. Today it is known to be comprised of 2 protons & 2 neutrons, but this was not known during Rutherford’s time. Rutherford did know that these particles are positively charged.
• Rutherford conducted an experiment now known as the ‘Gold Foil Experiment’. The observations from this experiment, formed the basis of the Rutherford/nuclear atomic model.
• Geiger & Marsden (Rutherford’s assistants) carried out an alpha scattering experiment as illustrated below:

                           

• The experiment involved bombarding an extremely thin piece of gold film with alpha radiation. The alpha radiation would penetrate through the gold & hit a fluorescent screen on the other side allowing us to determine if it had been deflected or not.
• Assuming Thomson’s ‘Plum Puddling Model’, the electrons are so small & randomly distributed that the larger alpha particle would pass through almost unimpeded by the atoms of the gold foil.
• However, it was observed that the alpha particles didn’t travel through unimpeded, they were actually deflected by the gold foil.

                   

• The deflection occurred mostly towards the middle of the beam. This indicated that there exists something at the centre of an atom, capable of greatly affecting the positively charged alpha particles.
• The large angles of deflection led to the alpha particle bouncing off in many different directions (even returning back to the source). The scientists had just observed the first evidence of an atom’s nucleus.

               

• In 1911, Rutherford proposed the planetary model of atoms based on the results obtained from his assistances’ experiment (the alpha-scattering experiment or the gold foil experiment).
• “An atom consists of a dense, minute, central core called the nucleus which carries positive charges. The small, negatively charged electrons are orbiting around the nucleus at a large distance”.

                                         

                   

 » The Proton

• Eight years after creating the nuclear atomic model, Rutherford would build on his atomic model with the discovery of the proton
• The experiment involved firing alpha particles at nitrogen gas. A particle roughly the same mass as a hydrogen atom was observed. This particle was deflected by an electric field with the opposing behaviour of an electron.
• Rutherford concluded that the particle was the electron’s counterpart & named this positive charge a proton.

      

※  There were however certain limitations related to Rutherford’s model:

• Firstly, if electrons (negatively charged) orbited a positive nucleus, why didn’t they exert an attractive force on each other? Newtonian mechanics predicted that the electron would emit EMR & lose energy until it fell into the nucleus.
• Rutherford’s model doesn’t explain another emerging phenomenon during the time; Absorption/ Emission Spectrum.

                 

 » The Neutron

• Rutherford identified a further problem with his own atomic model in the early 1920’s. If the nucleus was made of protons with similar charged, then why aren’t they repelled by each other?

※  Rutherford put forward two proposals to solve this problem:

1. There were electrons inside the nucleus to negate the repelling forces.
2. There was a neutral particle that could bind the protons together.

                                        

• James Chadwick (student of Rutherford) was the first physicist to prove the existence of the neutron. He interpreted the results of an experiment conducted earlier by Irene Curie & Frederic Joliot as evidence.
• Curie & Joliot showed that an unknown radiation (produced by Beryllium) was capable of knocking protons out of a sample of Paraffin wax. (Hydrocarbon)

       

• Chadwick used the law of conservation of momentum to conclude that the particle had to be as heavy as a proton.
• He then went on to show that the particle was uncharged, thus identifying the neutron as the last component of an atom.
• In summary, the atom is comprised of three major components. Currently represented by the Rutherford model.

                 

                         

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Quantum Mechanical Nature of the Atom

 » Introduction

• The most commonly used model of the atom is known as the Rutherford’s model. In this model electrons are seen revolving around a nucleus (made up of protons & neutrons).
• There was however one major physics principle that the model couldn’t explain;
• As electrons orbit the nucleus, they should emit energy, causing the orbit of the electron to shrink until they fall into the nucleus. Why does this not occur?
• Niels Bohr (1885 – 1962) was a Danish physicist trained under Rutherford.
• Drawing on the theories on quantisation (by Planck & Einstein) & the work of Anders Angstrom & Jacob Balmer, Bohr was able to present an atomic model that could explain the stable orbits.
• Anders Angstrom was the first physicist to calculate the wavelengths of four of the spectral lines for hydrogen. These were all in the visible part of the EM spectrum.
• Balmer then went on to derive a relationship between these wavelengths.

 » Balmer Series & Rydberg’s Equation

 

 » Bohr’s Atomic Model

• Bohr combined the work of Balmer/Rydberg with a quantum understanding to propose his atomic model.
• Hy hypothesised that in order for the electrons to not spiral into the centre, they needsed to exist in discreet & stable orbit (these orbits correspond to the n = 2, 3, 4, ... values from Balmer’s equation).
• In order to explain how the electrons remain in their stable orbits, Bohr that the electrons are not continuously emitting energy.

                                     

• Instead he proposes that electrons only emit energy when they transition from an excited state back down to a lower state. This process is what allows for the creation of an absorption spectrum.
• The amount of energy absorbed for each transition has a discrete value. (If a photon doesn’t supply that exact amount of energy the electron cannot make the transition).
• Using this information, the many possible electron jump can be mapped on an energy level diagram.
• The ground state represents the closest electron orbit from the nucleus (n=1).
• As n increases, the electron will move to an outer orbit, unit it becomes free from the electrostatic attraction of the nucleus (n = ∞). When this happens the atom becomes ionised.
• The different electron jumps are often grouped into series (e.g. the Balmer Series represents electrons jumping from an excited state down to n = 2 orbit, which releases visible light).

                

                                 

            

 » Limitations of Bohr’s Model

 ※  Whilst the model allowed for the explanation of stable orbits & emissions it had some limitations:

               

• The model accurately described how long atomic number atoms behaved, but was not as accurate for elements with many electrons, in many shells.
• The presence of a magnetic field caused strange observations to the absorption spectra. This could not be explained (Zeeman Effect).
• The model couldn’t explain how solids emitted a continuous spectrum.

• Whilst the Bohr model has imited applications, it was very important to help advanced the quantum approach to studying atoms.

 » Wave-Particle Duality of Light

• In 1905, Einstein’s Photon Theory demonstrated that the photoelectric effect could only be accounted for if light was assumed to have particle-like propoerties.
• However, the Wave Model of Light remained the only appropriate explanation for earlier observations of light (interference, diffraction, etc.).
• cientists were left with no other choice but to accept the dual waveparticle nature of light.
• Electromagnetic waves are characterised by their speed (c), frequency (f) & wavelength (𝜆):

                                              

• Electromagnetic particles (photons) are instead characterised by the energy they carry & their subsequent momentum:

                   

 » De Broglie’s Matter Wave

• By extension of Einstein’s Photon Energy (which claimed that EM waves could possess a particle nature), Louis de Brouglie in 1924 predicted that particles should also possess a wave nature.
• De Broglie hypothesised:

※ Matter has both wave & particle properties.

※ The wavelength associated with any particle with momentum p is:

                   

        

• The Broglie wavelength of an electron is smaller than that of visible light. The wavelength of everyday objects is even smaller due to their much larger mass.
• It is due to this reason that the wave nature of everyday objects does unnoticed.
• However, it should be possible to demonstrate the wave nature of a particle (such as an electron) by showing that it can be diffracted. Physicist set out to prove this wave nature of matter.
• Recall, that diffraction requires the aperture size to be comparable to the wavelength of the wave being diffracted.
• At the time te average aperture size of a diffraction grating ≈ 20𝜇𝑚 meaning it was extremely hard to observe electron diffraction.

                                  

 » Davisson & Germer’s Experiment

• In 1927, Davisson & Germer confirmed De Brogli’e momentum-wavelength postulate by observing that electrons diffracted through a crystal lattice.
• The De Broglie’s wavelength of an electron was simply too small to be diffracted through regular diffraction gratings.
• The spacing between Nickel atoms in the crystal lattice was small enough to produce observab;e diffraction effects.
• This clearly indicated the wave nature of electrons.

               

                                            

             

                              

 » Standing Waves

• Standing Wave: a pattern which results from the interference of two identical waves travelling along the same medium.

 » Impact of De Broglie’s Matter Wave

• One of the limitations of Bohr’s model was that it could not account for the stability of the electrons in its orbits (i.e. no scientific justification)
• Using the ‘matter wave’ proposal & the concept of electron standing waves, De Broglie provided a successful explanation to electron stability in Bohr’s discrete orbits.
• According to De Broglie, electrons are stable in its orbit around the atom because the electron wave forms a standing-wave pattern so the electron waves don’t interfere destructively. (NO ENERGY LOSS!!!)
• For the orbiting electrons to set up a standing-wave pattern, it must orbit the nucleus at allowable orbits/energy levels such that the circumference of the orbit equals to some integer multiple of the electron wavelengths:

                                  

                               

 » The Uncertain Nature of Matter

• After Bohr & De Broglie’s work physicist were beginning to find the dual nature of energy & matter hard to interpret & resolve.
• This is due to the fundamental difference between waves & particles; waves are continuous disturbance whilst particles are discrete. Particles should always exist in a single place in space, whilst waves spread out through space.
• The field of quantum mechanics was solidified, with an aim to study the duual anture of matter. The work of Schrodinger & Heisenburg set the foundations for future understanding.

 » Schrodinger’s Atomic Model

• In 1926, Erwin Schrodinger used a mathmetical model to describe the waveparticle duality of matter. His largest challenge was reconciling how particle (like electrons) can be continuous & discrete.

            

• The solution was to think of the wave nature of a particle as a probability known as the particle’s wave function.
• Schrodinger’s equation expresses the probability that an electron will occupy a certain region (or be in a certain state) around the nucleus of an atom.
• This is different to Bohr’s model as it doesn’t draw a circular path that the electron will definitely follow.
• Instead in 3D space the model shows regions where the electron has a high proability of existing (darker area) versus areas where there is a low probability of it existing (lighter area).                   
• Schrodinger’s atomic model is sometimes described as an atomic cloud. This quantum model is the most accepted current atomic model.
• Different electrons will have different probable locations. These location are called orbitals (different from orbits, which are only 2D) & are given specific names based on their shape.
• Each orbital can only have 2 electrons.

                                  

 » Heisenberg Uncertainty Principle

• The quantum model of the atom is also governed by the Heinsenberg uncertainity principle, which was propsed in 1926.
• The principle states that the position & momentum (& therefore velocity) of an object cannot be measured exactly at the same time.

※ This is not due to the accuracy of our measuring devices. It is mainly attributed to two things:

• The wave-particle duality of matter (particles are discrete while waves are continuous).
• The unavoidable interactions between an object being observed & the instrument doing the observing. (Observing an object involves imparting energy to it, that changes the nature of the observed object)

• This rule reaffirms the fact that we can only refer to location of particles in terms of probabilities.

 » Schrodinger’s Cat Though Experiment

• In 1935, Schrodinger proposed a though experiment as an analogy to the quantum nature of matter.
• The setup involves a cat placed in a sealed box along with a radioactive substance
• The substance has a 50% chance of detonating in the next hour (killing the cat) & a 50% chance of not detonating (not killing the cat).
• The question was, after an hour, is the cat dead of alive?
• The quantum interpretation of the situation would predict the cat is both alive & dead.
• This is of course an absurd observation. Cats cannot be both dead & alive.
• Schrodinger’s point (which is often missed) to show that it was crazy to apply the laws of small quantum objects (like electrons) to large complex objects (like cats).
• In summary, the work of Bohr, De Broglie, Schrodinger, Heisenberg (& others) have led to a complex & evolving field quantum mechanics. This is still very new & not well understood, but it has lead to large breakthroughs in science, computing & other areas.

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Deep Inside the Atom

 » Introduction

• Particle physics is a branch of physics that studies the nature of the particles that constitute matter & radiation.
• The fundamental building blocks of matter has evolved overtime from Dalton’s billiard ball model to the quantum cloud model. Sor far, we know that atoms are made of 3 fundamental particles: protons, neutrons & electrons.
• However in 1912, Physicists discovered mysterious particles bombarding Earth from outer space. The source of these new particles were called cosmic rays.
• Cosmic rays are fast & energetic. The particles that made up cosmic rays would strike atoms in the atmosphere creating strange new subatomic particles.
• As cosmic rays were unreliable, scientists started building machines capable of firing protons together to mimic the collision occurring in the atmosphere. These were called particle accelerators & they were responsible for discovering many additional particles.

                                    

                         

 » The Particle Zoo

• By the 1960’s, cosmic rays & particle accelerators had led to hundreds of different particles being discovered & named. This large number of different particles was collectively called the ‘the particle zoo’.
• Physicists started grouping these particles based on certain properties (charge – interaction with EF, spin – angular momentum, mass - matter & lifetime – time until it decays).
• To simplify these many particles, a more fundamental set of particles called quarks were hypothesised & then discovered. These particles form the basis of the standard model.

 » The Standard Model

• The Standard Model is a theory that classifies all know elementary particles (the fundamental building blocks of matter) along with the fundamental forces.
• There are three main components of the model:

※ Quarks

※ Leptons

※ Bosons

• Quarks & Leptons(fermions) are also divided into generations (I, II & III).

                         

• Besides from these standard particles the matter particles also have corresponding anti-matter particles (same mass, opposite charge). When a matter & anti-matter particle meet, they collide & annihilate each other (releasing huge amounts of energy).

 » Quarks

• Quarks are one of two families of fermions that make up matter. In total, 6 quarks have been discovered (up, down, charm, top & bottom).
• Protons & neutrons are composed of up & down quarks only. This implies that quarks can have fractional charges.

                                              

              

             

 » Leptons

• Leptons are the simplest & lightest subatomic particles. The first to be discovered is the electron.
• The muon & tau particles are larger counterparts of the electron. These particles quickly decay into electrons.
• This decay process also is accompanied by the production of neutrinos; incredibly small, neutral particles that are very abundant by rarely interact with matter.

 » Gauge Bosons

• Bosons differ from fermions; in that they are ‘force carrying particles’. These are responsible for carrying the fundamental forces:

                  

               

                                   

                                     

 » Evidence for the Standard Model

• Evidence for the standard model comes primarily from modern experiments conducted inside particle accelerators.
• The Australian Nuclear Science & Technology Organisation (ANSTO) operates the Australian Synchrotron (the Southern Hemisphere’s most powerful synchrotron).
• CERN is the world’s leading particle physics laboratory & houses the Large Hadron Collider (LHC), the largest particle accelerator ever constructed (diameter 27km).

 » Higgs Bosons

• Until the 1960’s physicists could not explain how subatomic particles gained their mass. The Standard Model did not explain the origins of mass or why some particles are very heavy while others have no mass at all.
• In 1964 Robert Brout, Fancois Englert & Peter Higgs proposed that all particles interact with an invisible field to gain their mass; the more a particle interacts with the field, the heavier it becomes.
• The Higgs Boson ≠ The Higgs Field

※  The Higgs Boson helps us detect the field.

※   The Higgs Field is the actual thing that gives particles mass.

• The Higgs Boson was added to the standard model, but we are still not entirely sure of its existence. However, the maths behind the standard model has always assumed that the Higgs Boson exists, meaning it is fundamental to the standard model.
• If the Higgs Boson could be observed, the standard model has further evidence supporting it.
• In 2012, scientists at CERN identified a particle in one their experiments that could potentially be the Higgs Boson. Since then, particle physicists had work to try & prove that this mystery particle is the Higgs Boson.
• This illustrates that the work on the standard model is still ongoing & incomplete.

              

 

Definitions

Formulas