quanta to quarks.docx

1Edwin TranQuanta to Quarks

Discuss both the evidence for and the limitations of Rutherford’s atomic model

Discuss the limitations of the Bohr model of the hydrogen atom, the spectra of larger atoms, the relative intensity of spectral lines, the existence of hyperfine spectral lines and the Zeeman Effect.

When alpha particles scattered at large degrees when a gold foil was within its path, Rutherford proposed that an atom consisted of a very small, dense, positively charged nucleus. The electrons were in orbit about the nucleus at distances very large compared to the dimensions of the nucleus.

One problem was that it was not mathematically explained. Furthermore it did not account for any of the properties of the electrons in the atom, in particular how electrons could be accelerating without emitting electromagnetic radiation. Also it failed to provide any information about the radius of the atom or orbital frequencies of the electron

While successful in explaining the wavelengths of the spectral lines in the hydrogen spectrum, Bohr’s model failed to account for:

o The spectra of larger atoms -The Rutherford-Bohr model only worked for hydrogen. It did not work for atoms with more than one electron.

o The relative intensity of spectral lines - Different spectral lines were different intensities. This could not be explained by the Rutherford-Bohr model.

o The existence of hyperfine spectral lines - It was found that some spectral lines consisted of much finer lines that when viewed at a low zoom appeared as one. The cause of these hyperfine spectral lines could not be explained by the Rutherford-Bohr model.

o The Zeeman Effect - The Zeeman Effect (the splitting of spectral lines when the sample was placed in a magnetic field) could not be explained by the Rutherford-Bohr model.

Discuss Planck’s contribution to the concept of quantised energy Planck said that energy was quantised in discreet packets of energy. This is given by the formula, 𝐸=h𝑓, where h is Planck’s constant. This means that the energy is a multiple of h and therefore quantised. This differs from classical physics where energy was thought to be a continuous wave. This concept of quantised energy was initially brought up for an explanation of black body radiation.

Define Bohr’s Postulates

1. Despite the nucleus (positively charged) and electron (negatively changed) being oppositely charged they do not attract and collapse together. The electrons are stable in their shells and are not pulled towards the nucleus. This violates classical physics. Also an electron that is stable and doesn’t change energy level will not radiate energy.

2. If an electron moves down an energy level, energy is released in the form of a photon. Similarly if an electron moves to a higher energy level then the atom must absorb some quanta of energy. This explains the existence of spectral lines

3. mvr=n h2π

where n is a positive integer. This means that 𝑚𝑣𝑟 (angular momentum) can only

take on certain values and is quantised.

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Perform a first-hand investigation to observe the visible components of the hydrogen spectrum

A hydrogen discharge tube was connected to high voltage electricity. The discharge tube was observed with a spectroscope. Spectral lines were observed. This process is shown in the diagram below.

The colours and wavelengths of the visible spectrum of hydrogen is shown below.




Discuss and quantify de Broglie’s proposal that any kind of particle has both wave and particle properties. Describe the confirmation of de Broglie’s proposal by Davisson and Germer and further explain the stability of the electron orbits in the Bohr atom using de Broglie’s hypothesis

De Broglie proposed that any moving object should have a wavelength given by :

λ=hmv

He proposed that wave and particle nature of light was inextricably linked. He then predicted that matter must also have a dual particle-wave nature.

De Broglie believed in the claim that it should be possible to observe the wave nature of a beam of electrons diffracted from the surface of a crystal. This impacted on the Davisson and Germer experiment.

In an experiment on reflection of electrons, the vacuum had a crack and nickel surface oxidised. Heat recrystallised the surface, forming crystals larger than the electron beam they used. When they shot the electrons, they saw diffraction which was a wave property. Electrons had both wave and particle characteristics and thus De Broglie’s idea was confirmed.

Define diffraction and identify that interference occurs between waves that have been diffracted

Diffraction refers to the spreading out of light waves around the edges of a small slit or aperture.

If two slits are open at the same time then the two waves will interfere (the interference is possible because of the diffraction pattern). The wave will be heightened in some places and cancelled out in other places.




Explain the stability of the electron orbits in the Bohr atom using de Broglie’s hypothesis Using de Broglie’s hypothesis of the wave nature of particles we can explain why electrons can only exist in specific energy levels. Because these orbiting electrons can be thought of as waves, where the shell number relates to the number of waves, if you have non integer number of waves then the wave will not join and will collapse. So electrons can only exist where a whole number of waves is possible. This coincided with the specific orbits that Bohr had postulated. Since the electron could exist as a wave it was in a non-radiating energy level as also postulated by Bohr.

n=5 n=4.5 n=4

If n=4.5, the waves would not join, therefore collapsing the orbit

Gather, process, analyse and present information and use available evidence to assess the contributions made by Heisenberg and Pauli to the development of atomic theory

Heisenberg: Heisenberg’s contribution to the development of atomic theory was the Uncertainty Principle, which states that both the position and the momentum of a subatomic particle cannot be accurately determined simultaneously. The more you know about the momentum of the particle, the less you know about its position. And the more you know about the particles position the less you know about its momentum. This can be expressed mathematically,

Uncertainty of momentum ×uncertainty of position≥𝑕2𝜋This is because the best methods we have to determine the position of a particle will change its momentum, and the methods used to determine momentum change the position. For example to see the position of the particle, we need to shine light on it to see it. However when photons are shown on the particle they collide and the momentum and path of the particle is changed by this collision.

Pauli: Pauli’s contribution to the development of atomic theory was the Pauli Exclusion Principle, which states that no two electrons in an atom can have the same set of quantum numbers. Pauli’s Exclusion Principle provides reason why electrons in atom are arranged in shells. An electron in an atom has four such quantum numbers. They define the energy of the electron in terms of the distance of its orbit from the nucleus, its orbit’s shape, the orientation of the axis of the orbit, and the electron’s spin on its own axis. He also explained the existence of the neutrino.




Discuss the importance of conservation laws to both (i) Chadwick’s discovery of the neutron and (ii) Pauli’s suggestion of the existence of neutrino.

(i) Chadwick’s discovery of the neutron

Chadwick analysed the work of Curie after she bombarded paraffin wax with the unknown radiation that was found by Bothe and Becker in 1930. From there he undertook experiments in examining the recoil of nuclei of hydrogen and nitrogen when hit by this unknown radiation. He then applied laws of conservation of momentum and energy to discover the neutron which was 1.15 the mass of the proton.

(ii) Pauli’s suggestion of the existence of neutrino

According to energy laws, when an atom undergoes beta decay, the energy of the emitted electron should fall within a relatively small range of energies. However, observed experimental results showed a large range, which seemed to defy the law of conservation of energy. To explain this, Pauli suggested the existence of a neutrino that was released concurrently with beta emission which possessed the missing energy to obey the conservation of energy law.

Define the components of the nucleus (protons and neutrons) as nucleons and contrast their properties

The nucleus of an atom is made up of protons, neutrons and other sub-atomic particles, known as nucleons. Protons have a positive charge and neutrons have no charge. The mass of the proton is slightly less than that of a neutron.

Symbol Charge (C) Mass (kg)Proton 1.602×10−19 1.673×10−27 Neutron 0 1.675×10−27

Define the term ‘transmutation’ Transmutation is the changing of one element into another by nuclear reactions, remembering that the number of protons in the nucleus of an atom determines the type of element.




Describe nuclear transmutations due to natural radioactivity Large unstable elements naturally decay into smaller elements in an aim to become more stable. During nuclear transmutations three forms of radiation can be emitted.

For example, Radium is an unstable element and goes through natural decay and thus, changes to the element Radon and hence, transmutation occurs.The natural nuclear radioactive decay of uranium-238 is shown below.

Describe Fermi’s initial experimental observation of nuclear fissionNuclear fission is the splitting of an atom into other smaller elements of the atom. Fermi bombarded Uranium-235 with neutrons and saw that the slower the neutron travelled, the more effective nuclear reactions occurred. He observed that Kr-92 and Ba – 141 was produced as a result of the Uranium atoms becoming unstable. Two lighter elements occurred and thus it was nuclear fission. He also observed that more neutrons were produced.




Explain the significance of mass defect to atomic physics using Einstein’s equivalence between mass and energy. Also, compare requirements for controlled and uncontrolled nuclear chain reactions with specific reference to fission reactors and describe Fermi’s demonstration of a controlled nuclear chain reaction in 1942.

Mass defect is the difference between the mass of the constituent nucleons and nucleus. This mass defect is responsible for the energy as per (E =mc2), which is the energy to bind the reactants (often referred to binding energy).

A critical mass of fissile material is required for self-sustaining chain reaction. To create a self-sustaining nuclear reaction, each fission reaction requires the release of an average 2.5 neutrons to continue the process. An appropriate isotopic mix e.g. U235/238 (Uncontrolled). Control rods (steel cadmium), that absorb neutrons are inserted into a fission reactor to slow or stop the chain reaction completely, or removed to allow more reaction (controlled)




Femi demonstrated this controlled reaction by slowly withdrawing cadmium control rods, 15 cm at a time, while reaction count was measured. Rate of fission and prediction of when reaction was self-sustaining were calculated

Evaluate the relative contributions of electrostatic and gravitational forces between nucleons

Nucleons are protons and neutrons. Protons are positively charged and so their force of electrostatic repulsion is repelling them. This force is quite large. The other force acting on protons is the force of gravity. But this force is very weak because the mass of a proton is very small. Two protons in a nucleus are about 10−15 m apart, and so the force of gravity between these two protons will be about 1.9×10−34 N, of attraction. But the electrostatic force is about 230 N, of repulsion. This means that the force of gravity is nowhere near large enough to hold these protons together in the nucleus. Neutrons have the force of gravity as attraction but this again is extremely weak. Neutrons have no electrostatic force because they are neutrally charged.

Account for the need for strong nuclear force and describe its propertiesSo how can protons exist together in the nuclear with such a strong force of electrostatic repulsion? Well this is where the strong nuclear force comes in. It is this strong nuclear force that holds these protons together in the nucleus. This strong nuclear force acts on both protons and neutrons1.

As seen in the graph, the typical nucleon separation has a strong nuclear force of 10^4 N where as the electrostatic force is 250 N. This shows that the strong nuclear force is able to hold together the nucleons with ease. However, as the the nucleon separation becomes smaller, the strong nuclear force becomes a repulsive force and as it gets further, it becomes weaker.

Explain the concept of a mass defect using Einstein’s equivalence between mass and energy

The mass of protons and neutrons can be measured to be 1.673×10−27 kg and 1.675×10−27 kg respectively. The mass of a nucleus of an atom can also be measured. Take helium as an example, it is made up of two protons and two neutrons in the nucleus and its atomic mass is 4.003 amu. However when we add the mass of two protons, two neutrons and two electrons we get a mass of 4.031 amu. This is slightly greater than the measured mass of the atom. The difference in these two masses is known as the mass defect, i.e. mass defect helium is 0.028 amu.




We know that the conservation of mass must hold, so where does this mass go? Well it is converted into energy (𝐸=𝑚𝑐2) called the binding energy which holds the atom together. The graph below shows the binding energy per nucleon graphed against mass number.

Describe Fermi’s demonstration of a controlled nuclear chain reaction in 1942

In 1942 Fermi managed to attain a controlled nuclear chain reaction in a squash court at the University of Chicago. He used the entire nation’s supply of uranium to do this. Control rods were known to be neutron absorbers and were inserted amongst the uranium. This was done to prevent the reaction from becoming uncontrollable and unstoppable. Geiger counters were used to detect the radiation emitted from the nuclear fission. Neutrons were shot at the uranium and it was noticed that by placing control rods in between the uranium, the detected radiation stabilised and continued at this stable rate. Fermi had achieved a controlled nuclear chain reaction.

Working from secondary sources discuss the operational principles and radiation observed to be emitted from a nucleus using a Wilson Cloud Chamber or similar detection device

A Wilson cloud chamber consists of supersaturated vaporised alcohol or supersaturated vaporised water. It uses the ionising ability of radiation, to differentiate between alpha radiation, beta radiation and gamma radiation. The process of this utilisation begins when radiation is fired into the chamber. This radiation causes the ionisation of atoms as it passes. The vapour condenses at the ions and the radiation hence leaves behind a vapour trail which can be analysed to determine radiation type. Alpha radiation is observed to have a thick and short trail (figa). Beta radiation is observed to have a thinner and longer trail than alpha (figb). Gamma radiation has the thinnest and longest trail.

Describe the use of a named isotope in each of the medicine, agriculture and engineering application areas.

Gamma radiation from technetium-99m is a diagnostic tool used to test for blood clots and problems with circulatory system. Small dosages of gamma radiation are detected from the gamma camera. Technetium-99m has a short half life of 6 hours to reduce damage to the patient

Gamma rays from Co-60 are used to sterilise food products and extend their shelf life significantly. Radiation kills the bacteria/viruses that cause decomposition of substances. Cobalt-60 has a half life is 5.3 years

A common application of radioisotopes is the use of americium-241 in smoke detectors. It emits alpha (half life of 432.7 years) particles that ionise the air between two plates that have a potential difference. If smoke interferes with the air, it will get attracted to the ionised air particles and change the current flow. This change sets off the alarm



quanta to quarks.docx

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