“Modern Physics – Models of the Atom”;
Modern Physics
Models of the Atom
BOHR MODEL OF THE HYDROGEN ATOM
In 1913, Niels Bohr introduced his atomic Hydrogen model made of a positively charged nucleus
containing protons and neutrons, surrounded by electrons travelling in circular orbits around the
nucleus. This model was a major step in understanding quantum theory, however is incorrect with
the description of election orbits. Treating the electrons like planets orbiting in a solar system, Bohr
suggested that there was a definite radius and momentum that the electrons followed, which is
incorrect. There was also no description as to why certain spectral lines were brighter than others.
PHOTON
Photons are fundamental particles of light, having properties of both a particle and a wave, it allows
for refraction and diffusion. However, unlike elementary particles, photons are theorised to have no
mass carrying no charge. They are the most visible part of the electromagnetic spectrum, leading
to the photoelectric effect making solar power possible. The photoelectric effect working when
photons hit an atom, causing it to lose an electron, creating electricity.
QUANTISATION OF ENERGY
The quantisation of energy is the absorption or emission of energy. It is dependent of the intensity
of the electromagnetic energy, as it increases or decreases, instead of following a smooth curve, it
steps up or down from a quantised level to another. Max Planck determined a mathematical model
which described this, as it could not be explained through the traditional laws of physics. The
absorption or emission was based on a constant of 6.62×10-34 joule-seconds, also known as the
Planck’s constant. Later in 1905, Einstein made a formal to determine the quantised energy level
of a photon travelling on a beam of light, E=hf where E is the energy contained in a single photon,
h is the Planck’s constant, and f is the photons frequency.
DISCRETE ATOMIC ENERGY LEVELS
Electrons in a Hydrogen atom must be in energy levels. These energy levels are be discrete. The
value of energy of the electron, for the first energy level is -13.6 eV. The electrons must have
exactly that amount of energy to be in that particular energy level, it cannot have a value of energy
that is different.
ELECTRON TRANSITION BETWEEN ENERGY LEVELS
Electrons can transfer between these energy levels but needs to gain energy if moving from a
lower energy level to a higher one. If the electron is moving from the first energy level to the
second, it would require 10.2 eV of energy. The electron gains the energy by light absorption. It is
the opposite if the electron moves from the second energy level to the first, as energy must be lost
and therefore light must be emitted. The light that is emitted or absorbed to move between the first
and second energy level is a photon with exactly 10.2 eV of energy. The energy that a photon
carries is dependant on its wavelength. This wavelength can be found from the equation, E = hc/l,
where E is the energy of the photon, h is Planck's constant and c is the speed of light. Using this
equation, the wavelength of the photon which has 10.2 eV is 1.21×10-7 m. This means it is from the
ultra violet part of the spectrum. So when electrons move between the first and second energy
levels of a Hydrogen atom, a photon of ultra violet light must be emitted or absorbed. The energy
required for electrons to move between the second and third energy levels is less, and so on for
further energy levels. If the electron gained enough energy to require 0 eV, it would be free from
the Hydrogen atom making it an ion as it is missing an electron.
IONISATION
To form an ion, there has to be an addition or subtraction of an electron within the atom. Losing an
electron causes a positive ion as there is more protons then electrons, causing an overall positive
charge. Adding an electron causes a negative ion as there is more electrons then protons, causing
an overall negative charge.
ATOMIC LINE SPECTRA
When atoms absorb or emit electromagnetic radiation,
light, these have discrete energies that correspond to the
atom absorbing or emitting them. When the light is put
through a prism, according to the wavelength of said light,
it is separated. On a continuum spectrum, bright lines
correspond to an emission spectrum, and dark lines
correspond to an absorption spectrum.
ELECTRON VOLT
An electron volt is when an electron is accelerated through an electric potential difference of 1 volt,
where it gains one electron volt of energy. This approximates to 1.6×10-19 Joules. Electron volts are
used to measure energy of electromagnetic radiation, in the x-ray and gamma-ray wavebands of
the electromagnetic spectrum.
Photo-Electric Effect
DISCOVERY
in 1887, German Physicist Heinrick Hertz observed ultra violet light shining on 2 metal electrodes
with a voltage applied across them, the light changes the voltage and sparking occurs. This was
the beginning of the photoelectric effect, as there was clear relationship between light and
electricity. However in 1902, Philipp Lenard clarified the photoelectric effect by showing that
electrically charged particles can be freed from a metal surface when it is illuminated. These
particles behaved exactly like electrons. Albert Einstein went on to clarify the photoelectric in 1905
with the formula E=hf, mentioned above. Arthur Compton, in 1922, treated x-rays as photons and
measured the change in wavelength as they interacted with free electrons. In 1931, Ralph Fowler
suggested the relationship between a photoelectric current and temperature in the metal. It was
later found that photons could also emit electrons in insulators, which aren't electrical conductors.
APPARATUS USED
This was the apparatus used to show the photoelectric effect.
There are two metal plates with a charge applied on them,
photons hit these metals and cause electrons to be emitted.
The metal plates are in an evacuated glass cube so no external
forces act on the effect.
RELATIONSHIP BETWEEN PHOTON AND ITS WAVELENGTH
There is an inverse relationship between the energy in the
photon and the wavelength of light given by the following equation, E=hc/λ, where E is the energy
of the photon, h is Planck’s constant, c is the speed of light, and λ is the wavelength of light. This
inverse relationship states if the energy of the photon is high, the wavelength of light will therefore
be short. The opposite for low energy photons, the wavelength will be long. Shorter wavelengths
will consist of light towards the blue end of the spectrum, whereas longer wavelengths will consist
of light towards the red end of the spectrum.
WORK FUNCTION
The work function is the minimum amount of photon energy needed to free
an electron from a substance. Different substances have different work
functions, measured in eV. The following table has the work functions of
commonly used substances for the photoelectric effect.
THRESHOLD ENERGY
The threshold energy is the minimum amount of energy required to free an
electron from the atom. The energy of the electron is given by the equation
is Ek=hf-Φ. If photons have a smaller total energy compared with Φ, no
electrons will be emitted, however if the photons have a greater total
energy compared with Φ, electrons will be emitted with kinetic energy.
KINETIC ENERGY OF ELECTRON
Once the electron has been emitted, it may still contain energy. The
minimum amount of energy used by the electron in ionisation is known as
the threshold energy. However there is still more energy contained within
the electron if the photon provides more energy then is required to
overcome the work function, and that energy is used for the kinetic energy
of the electrons. This is for when the electron is released from the atom
and moves away.
PHOTOVOLTAIC SYSTEMS
Photovoltaic systems consist of semiconducting materials which convert
solar energy into electricity. The system uses solar panels which are made
of solar cells to supply solar power. This system uses a two part process,
the first part involving the photoelectric effect, described above, and the
second part involving the ionisation of crystallised atoms, generating an electric current. This
process is using a renewable power source, the sun, is cheap to manufacture and is currently
being implemented in certain parts of Europe. It is an ideal replacement for current forms of power,
fossil fuels and coal, as the energy the sun provides will be an ever lasting source. At the rate of
use, currently with fossil fuels and coal, we will run out of those resources within the next few
decades and photovoltaic systems will be the perfect replacement. The only problem with this
system, is the availability of sun throughout the year. During summer and spring, this system would
be great as there would be longer days, with more exposure to the sun. However during winter and
autumn, there would be shorter days, with presumably less exposure to the sun. Current
technology doesn't allow for great storing of electricity that has been converted from solar power,
and if that was improved, photovoltaic systems should be implemented across New Zealand. Once
gaining approval from the government, PV panels should be put up on every roof, allowing for
maximum absorption of solar energy. There are already improvements being made to current
panels, to minimise costs by making the panels out of cheaper materials, so that this technology is
available to everyone. Once PV panels are introduced into homes, it should also be introduced to
cars, as that is one of the biggest users of non renewable resources.
Nuclear Reactions
COULOMBIC REPULSION BETWEEN NUCLEONS
In the nucleus, there are protons and neutrons. These are collectively called nucleons, and are
held together in the nuclei by the nuclear force. The protons and neutrons experience the nuclear
force almost identically. Neutrons are neutral and have no charge, whereas protons are positive
and have a charge of +1, and therefore experience a coulombic repulsion. With this repulsion, the
protons will be pushed apart, however the nuclear force is strong enough to overcome the
electromagnetic repulsive force.
BINDING ENERGY AND MASS DEFICIT
The binding energy is the energy required to split the nucleus of an atom into protons and
neutrons. This will always be positive, as all nuclei require energy to separate them. This binding
energy accounts for a difference between the actual mass of the atoms nucleus and the expected
mass based on the sum of masses of the non bound parts if the atom.
CONSERVATION OF MASS FOR NUCLEAR REACTIONS
There is a law of conservation of mass during all physical and chemical reactions. This dictates
that the total mass of products is equal to the total mass of the reactants. However in nuclear
reactions, conservation of mass can’t work as some of the mass is being converted into energy.
The law must therefore be the total mass of products is equal to total mass of reactants that have
not undergone a nuclear reaction where some of the mass has been converted into energy.
EINSTEINS EQUATION
Alert Einstein developed the special theory of relativity in 1905, represented by the formula E=mc2,
where E is energy mass can be converted into, m is the mass, and c is the speed of light. The
implication of this equation was that mass and energy are interchangeable. This equation is the
key in terms of nuclear power as small amounts of mass can be converted into huge amounts of
energy.
FUSION VS FISSION
There are two types of nuclear reactions, fusion and fission. Fusion is the conjunction of two light
atoms into a heavier one, whereas fission is the disjunction of a large atom into two smaller ones.
Fusion does not produce a lot of radioactive particles whereas fission does. The environment for
fusion to occur involves high density, and high temperatures whereas fission requires critical mass
of the substance as well as high speed neutrons. The energy required for fusion to work is high ass
it takes a lot of energy to bring two protons so close that the nuclear forces overcome electrostatic
repulsion. However it does not take a lot of energy to split two atoms in a fission reaction. Fusion
releases huge amounts of energy, whereas fission reactions don’t release as much. Currently
fusion is still experimental technology for energy production, however fission is used in nuclear
power plants. The primary fuel for fusion reactions are experimental hydrogen isotopes, whereas
uranium is used in fission. Although fusion is still experimental, getting conditions right is extremely
difficult. Fission reactions creates a lot of waste material, for not a lot of energy, compared with
fusion, which is very dangerous, unless handled properly. The waste material produced by fission
currently will take thousands of years to decay to a level that is safe, because of the half life
equation. Currently New Zealand is nuclear free, however with advancements in technologies,
nuclear reactors could be a way to power New Zealand. If a proper waste management system
was made, fission reactors would a great power source to replace fossil fuel per in New Zealand,
however, strict protocols would need to be put in place so that catastrophic events would happen.
Fusion reactors could also be a good replacement for current fossil fuels, however a safe way to
merge two atoms in the correct conditions would need tho be discovered, and methods to contain
such a huge energy source would also need to be found. As fusion would create significantly more
energy then fission, it would better replace fossil fuels in New Zealand. The problem with these
nuclear based power sources in New Zealand is, a lot of things still need to be done to make it
even possible, let alone safe. It would be much better then fossil fuels and photovoltaic panels,
even more safe, provided current obstacles were overcome, however while that happens, I think
that photovoltaic panels are a suitable replacement for fossil fuels, especially since we have the
technology available right now. If and when, the problems that nuclear power sources currently
face are overcome, nuclear power, especially fusion, would be an ideal power source for New
Zealand.
Resource Page
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"4"
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website "2"
ESA Level