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9.8 Option - From Quanta to Quarks: 3. Fermi and Chadwick: The nuclear age begins

Syllabus reference (October 2002 version)
3. The work of Chadwick and Fermi in producing artificial transmutations led to practical applications of nuclear physics	Students learn to: define the components of the nucleus (protons and neutrons) as nucleons and contrast their properties discuss the importance of conservation laws to Chadwick’s discovery of the neutron define the term 'transmutation’ describe nuclear transmutations due to natural radioactivity describe Fermi’s initial experimental observation of nuclear fission discuss Pauli’s suggestion of the existence of neutrino and relate it to the need to account for the energy distribution of electrons emitted in ß-decay evaluate the relative contributions of electrostatic and gravitational forces between nucleons account for the need for the strong nuclear force and describe its properties explain the concept of a mass defect using Einstein’s equivalence between mass and energy describe Fermi’s demonstration of a controlled nuclear chain reaction in 1942 compare requirements for a controlled and uncontrolled nuclear chain reaction	Students: perform a first-hand investigation or gather secondary information to observe radiation emitted from a nucleus using Wilson Cloud Chamber or similar detection device solve problems and analyse information to calculate the mass defect and energy released in natural transmutation and fission reactions

Extract from Physics Stage 6 Syllabus (Amended October 2002) © Board of Studies, NSW.
[Edit 2 July 09]

Prior learning: Preliminary modules 8.5, 9.4.

Background: Today, nuclear power is taken for granted. In some countries it supplies up to 40% of electricity yet our understanding of how energy can be released from the atom was poorly understood until the period just before the Second World War. The scientific impetus to invent new weapons and massive government financial support led to much more detailed understanding of the structure of the atom.

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

Protons and neutrons are nucleons. Protons carry a charge of 1.602 × 10^-19C. Neutrons carry no charge. Protons have a mass of 1.673 × 10^-27 kg. Neutrons are slightly more massive with a mass of 1.675 × 10^-27 kg.

perform a first-hand investigation or gather secondary information to observe radiation emitted from a nucleus using Wilson Cloud Chamber or similar detection device

You will only do this dot point as a first-hand investigation if your school has a Wilson Cloud Chamber and has access to suitable radioactive material. If this is the case all safety precautions for using radioactive material will have to be followed.
Secondary information can be gathered from the Internet, from Physics texts or from appropriate scientific journals. A starting point could be The Cloud Chamber C R Nave, HyperPhysics, Department of Physics and Astronomy, Georgia State University, USA and the experiment done by Wilson is explained here Department of Physics, Brown University, Providence, Rhode Island, USA

discuss the importance of conservation laws to Chadwick’s discovery of the neutron

Background information

As early as 1907 and definitely in 1920, Rutherford proposed the presence of a neutral particle in the nucleus. That proposal was based largely on the fact that the mass of the nucleus of small elements had been measured and was found to be greater than the mass of the number of protons they contained. The presence of the neutron was also suggested by the discovery of isotopes.

Soddy, in 1907, suggested that atoms of the same element might contain different numbers of neutrons without affecting their chemical nature. This was able to account for the non-integral atomic weights of certain elements.

In 1912, Aston used a primitive mass spectrograph to show that neon of atomic weight 20.2 atomic mass units (amu) had two isotopes of atomic weight 20 amu and 22 amu respectively. This could only be explained by virtue of the law of conservation of mass if the nucleus contained neutral particles of some form.

In 1930, Bothe and Becker of Germany found that beryllium under alpha bombardment emitted radiations of great penetrating power. It was thought they were gamma rays because they apparently did not have a charge.

Frederic Joliot and his wife Irene Joliot-Curie, who was the daughter of Pierre and Marie Curie, found that this radiation could expel protons from paraffin wax, a dense hydrocarbon, and calculated that the energy of any such γ-rays would need to be about 50 MeV. This was unreasonably high.

The idea of using the uncharged radiation to eject protons was so that the uncharged radiation that was difficult to detect would be detectable because protons were easily detectable in experiments using an ionisation chamber.

In 1932, James Chadwick suggested that the highly penetrating radiation was Rutherford's neutral particle from within the nucleus. Chadwick thought that a neutral particle of mass about 1 amu could expel protons from hydrogen compounds much more efficiently. His measurements of the momenta and energies involved in these and other nuclear reactions confirmed that these neutrons actually existed.
His experimental work on the nature of the uncharged radiation used conservation of momentum and energy laws to show that the neutron had a mass of just slightly more than that of a proton.

define the term ‘transmutation’

Transmutation is the process responsible for transforming one element into another. This occurs by the emission of an α or β-particle from the nucleus in natural transmutations.

solve problems and analyse information to calculate the mass defect and energy released in natural transmutation and fission reactions

Background information

This idea is based on the use of Einstein's equation for the mass defect , E= mc².

Using this equation, it is possible to determine the mass defect for every 1 atomic mass unit (u) converted to energy, approximately 931 MeV of every 1u of mass. The energy release comes about because during fission the total mass of the products is less than the total mass of the reactants with the difference being converted to energy.

To solve this type of problem you will need to know the total mass in atomic mass units (u) of the element undergoing fission including the mass contribution from its binding energy and the total mass of the elements and subatomic particles that are the products of the fission.
Analysing the information, the difference in the atomic mass units before and after the fission in u can be multiplied by 931 MeV to give the energy released in a fission reaction.

describe nuclear transmutations due to natural radioactivity

Natural transmutations involve the emission of α-particles or β-particles from the nucleus of a radioactive atom.
An example of α-decay
Note how the atomic mass falls by 4 and the atomic number by 2 with the emission of the α-particle to form a new element.
An example of β-decay
Note how the atomic mass remains the same but the atomic number increases by 1 when a β-particle is emitted.

describe Fermi’s initial experimental observation of nuclear fission

In 1934, the Italian-American physicist, Enrico Fermi used the observed half lives of radiation emitted by atoms bombarded by neutrons to identify the element as having an atomic number higher than 92 which is uranium. This was an observation of nuclear fission.
In 1942, Fermi built the first atomic pile in a converted squash court at the University of Chicago. He used 6 tonnes of uranium metal (the entire nation's supply) and 40 tonnes of uranium oxide separated by 385 tonnes of graphite bricks. Control rods of cadmium, known to be a good neutron absorber, were inserted amongst the uranium and graphite bricks to prevent the chain reaction from becoming supercritical. The experiment was successful and the primitive unshielded nuclear reactor generated 0.5 W of thermal power.

discuss Pauli’s suggestion of the existence of neutrino and relate it to the need to account for the energy distribution of electrons emitted in ß-decay

The electrons emitted in the process of beta decay have different energy levels. They are all generated in a similar process whereby an electron is emitted from a neutron to leave behind a proton in the transmutation process of increasing the atomic nucleus of an atom by 1 atomic mass unit but causing only a small difference to the atomic mass.
The problem facing Pauli was simply that although the process was the same from the same element, why and how could the range of energies of the electrons be explained. The same transmutation reaction should release beta particles of the same energy level.
To overcome this problem, Pauli assumed the release of another particle, the neutron (later called the neutrino by Fermi), which was released at the same time as the beta particle. This particle although not detected was thought to be neutral and to carry an amount of energy that was equivalent to the amount of energy that was less than the maximum kinetic energy possible for an ejected beta particle produced in a particular transmutation.

evaluate the relative contributions of electrostatic and gravitational forces between nucleons

The gravitational and electrostatic forces are both inverse square forces, although their effects in the nucleus are opposite. At the small distances of separation between the proton and neutrons in the nucleus the gravitational attraction due to the mass of these particles should be high.
The electrostatic forces between the protons where like charges repel should also be high at the minimum distances of separation in the nucleus. Calculation of the relative calculation of these two oppositely directed forces leads to a finding that the electrostatic force is by far the stronger of the two forces. This should cause the nucleus to fly apart and become unstable for all elements except hydrogen. Clearly this doesn't happen so another force is required to explain why the nucleus stays together.
To stabilise the nucleons in the nucleus another force termed the strong nuclear force is required.

account for the need for the strong nuclear force and describe its properties

The strong nuclear force is needed to account for the stability of the nucleons in the nucleus and to overcome the repulsive electrostatic force due to proton- proton repulsion. The properties required of such a force include:
- The force is strong enough to be able to overcome the electrostatic force.
- The force is independent of charge. It acts between proton-protons and proton-neutrons.
- The force is able to account for an even spread of matter and hence density of nucleons in the nucleus. To do this the force must be a short-range force acting only between immediate neighbour nucleons.
- The force is carried by the messenger particle called the pi meson. This particle is 273 times heavier than an electron.

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

When the C-12 standard was established, it was not anticipated that the nuclear masses of other nuclides would be perfectly integral numbers of amu's. The truth turned out to be that measurement confirmed that the nuclear mass of any isotope is invariably less than the total mass of its constituent protons and neutrons.
This missing mass is referred to as the mass defect of the nucleus. This mass defect as measured is invariably negative.
By the time this feature was recognised, Albert Einstein had produced his General Theory of Relativity in which he argued that mass and energy were interconvertible under the now famous relation E = m c² , where c is the speed of light in a vacuum, which Einstein regarded as the universal constant. Einstein did not suggest that whole bodies of matter could be converted to energy, but rather that a body possessing kinetic energy would effectively have a relativistic mass which was greater than its rest mass by the mass-equivalent of that kinetic energy: m = m_o + E/c²
Similarly, a composite body like an atomic nucleus composed of protons and neutrons held together by cohesive forces possesses potential energy and would have an effective mass less than the total mass of its constituent parts if measured separately:
The mass defect of a nucleus is the mass-equivalent of the energy of formation/dissolution of the nucleus which in turn is equal to the binding energy of the nucleus.

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

In 1942 Fermi, built the first atomic pile in a converted squash court at the University of Chicago. He used 6 tonnes of uranium metal (the entire nation's supply) and 40 tonnes of uranium oxide separated by 385 tonnes of graphite bricks. Control rods of cadmium known to be a good neutron absorber were inserted amongst the uranium and graphite bricks to prevent the chain reaction from becoming supercritical. The experiment was successful and the primitive unshielded nuclear reactor generated 0.5 W of thermal power.

compare requirements for a controlled and uncontrolled nuclear chain reaction

The essence of a controlled fission reaction is that each fission that occurs should produce one and one only further fission of another nucleus. Such a perfectly controlled reaction is called a critical reaction and the amount of fissionable material of given purity that can provide that one-for-one capture probability is called the critical mass.
An uncontrolled fission process involves a process whereby more than one nucleus is caused to undergo fission as a result of the fission of a single nucleus. This type of reaction is produced in an atomic bomb. For such a reaction to occur the amount of fissionable material of a given purity brought together in one lump must exceed the critical mass.