Nuclear physics for OCR A-level Physics
This page covers the following topics:
1. Stable nuclei
2. Unstable nuclei
3. Excited states
4. Closest approach method
5. Electron diffraction
6. Nuclear radius
A stable nucleus is a nucleus who has enough nuclear energy to hold the elements of the nucleus together permanently. There is a strong nuclear force that is attractive and is short range, which is stronger than the repulsive forces between the protons. At extremely short distances, there is a repulsive force between the protons and the neutrons so that the nucleus doesn't collapse. The N-Z ratio is the neutron-proton ratio of a nucleus, ie. the number of neutrons to its number of protons. The N-Z ratio increases with increasing atomic number for stable nuclei.
Unstable nuclei are nuclei whose nucler forces aren't strong enough to generate enough energy to hold the nucleus together permanently. This is due to the fact that unstable nuclei have an excess of either protons or neutrons. To become stable, unstable nuclei emit particles or radiation, and thus they are radioactive. The nuclei can emit alpha particles, beta particles and gamma particles. On the N-Z curve, unstable nuclei which lie above the curve are called neutron-rich, whereas ones which lie below it are called neutron-poor. Neutron-rich nuclei become more stable by losing neutrons through beta decay, which increases the proton number by 1 and decreases the neutron number by one. Neutron-poor nuclei become more stable by gaining neutrons, which decreases the proton number by 1 and increases the neutron number by 1.
Electrons inside an atom are held on energy levels around the nucleus, ie. they are held at fixed distances from the nucleus. Atoms go into their excited states when enough energy is absorbed by atoms so that an electron moves to a higher energy level. The atom is said to be excited, and this only occurs when the electron receives the exact amount of energy required to move to a higher energy level. For an electron to return to its ground state, gamma radiation must be emitted. This radiation will have the energy which is the difference between the two energy levels. Due to the different arrangements of different electrons, the emission of gamma radiation from different atoms will be of different colours. Ioanisation is when an electron is given enough energy to be removed from the atom.
When positively charged alpha particles are fired towards a nucleus, they get repelled due to the repulsive force between them and the protons in the nucleus. Alpha particles start off with kinetic energy. Due to the repulsion force, the alpha particles will get slower as they approach the nucleus, so the kinetic energy will turn into electric potential energy. The distance of closest approach is the distance at which the alpha particles will get repelled and turn back. This distance is equal to the radius of the nucleus and can be calculated using Coulomb's equation. A typical radius for a gold nucleus is 4.5 × 10⁻¹⁴ m.
The model an atom before the one currently perceived as correct was the plum pudding model, which described the atom as a positive "pudding" material with negative "plums" distributed throughout. The Rutherford scattering experiment changed this. Rutherford fired alpha particles at a thin gold foil and made three key observations. Most of the alpha particles went straight through, some were deflected back through large angles and very few were deflected backwards. This led to the new model of the atom, which states that the positive material is concentrated in a small, massive region called the nucleus, and the negative electrons are orbitting around it. Electron diffraction is carried out by firing electrons at a sample and observing the resulting interference pattern. Electrons are said to have wave-particle duality, meaning that it has both wave and particle properties, thus an interference pattern will be observed.
The total number of nucleons in a nucleus is called the mass number. It can be found using the equation A = Z + N, where A is the mass number, Z is the number of protons and N is the number of neutrons. Assuming that the volume of a nucleus is spherical and given by V = 4πr³A/3, nuclear density can be calculated using ρ = 3u/(4πr³), where r is the constant of proportionality 1.05 × 10⁻¹⁵ and u is the atomic mass unit, 1.66 × 10⁻²⁷ kg. This shows that nuclear density is constant, thus nuclei of all atoms are the same. It can be concluded that the nucleons of an atom are separated by the same distance regardless of the size of the nucleus, meaning that they are evenly distributed.
Sketch a diagram to show Rutherford's scattering experiment.
What is the property of electrons that allow for electron diffraction to occur?
Electrons are said to have wave-particle duality, meaning that it has both wave and particle properties, thus an interference pattern will be observed and electron diffraction will occur.
What is the N-Z ratio?
The N-Z ratio is the neutron-proton ratio of a nucleus, ie. the number of neutrons to its number of protons.
Explain what happens when an alpha particle gets fired towards a nucleus.
When positively charged alpha particles are fired towards a nucleus, they get repelled due to the repulsive force between them and the protons in the nucleus. Alpha particles start off with kinetic energy. Due to the repulsion force, the alpha particles will get slower as they approach the nucleus, so the kinetic energy will turn into electric potential energy. Once the alpha particle reaches the distance of closest approach, the alpha particles will turn back.
An electron is on the first energy level in an atom. Given that the energy difference between the first and second energy levels is −7.8 eV, state the amount of energy that is needed by the electron to move to the second energy level.
Excitation only occurs when the electron receives the exact amount of energy required to move to a higher energy level. Therefore, the electron needs 7.8 eV of energy.
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