IB Physics/Atomic and Nuclear Physics

7.1 Atoms and their constituents

Atomic structure

7.1.1 Describe a model of the atom that features a small nucleus surrounded by electrons.

• The atom is spherical in shape composed of a small and dense nucleus.
• The nucleus is composed of protons (that have a positive charge) and neutrons (that have a neutral charge).
• The nucleus is orbited by "shells" of electrons.
• The electrostatic attraction between the electrons and the nucleus keep the atom together.

7.1.2 Outline the evidence that supports a nuclear model of the atom.

The Geiger-Marsden experiment supports the current nuclear model of the atom. The alpha particle scattering experiment (by Rutherford/Geiger+Marsden) involved firing alpha particles at a sheet of very thin gold foil, and detecting where they went (with a screen). The results of the experiment were that the majority of alpha particles passed straight through. Of those which were deflected, many were deflected through very large angles, and even straight back at the source. This result suggested that atoms consisted mostly of empty space, with a small nucleus of high positive charge.

Results of Geiger-Marsden experiment	Explanation of results
Most particles passed through the gold foil	The atom is composed mostly of space
A small percentage of the particles deflected at 0º-90º	The gold nucleus is positive. Alpha particles are repelled by the nucleus, causing its path to deflect at an angle.
A small percentage of the particles "bounced" back at an angle larger than 90º	The alpha particle collided with the gold nucleus.

7.1.3 Outline one limitation of the simple model of the nuclear atom

Firstly, the simple model of the nuclear atom is that there is a small nucleus surrounded by orbiting electrons (there are no electron shells). According to the theory of electromagnetism, an accelerated charge should radiate electromagnetic waves and thus lose energy.

Rutherford's model was that around the small, highly charged nucleus, electrons orbited like planets around the sun. This created many more questions. Why didn't the electrons emit radiation and lose energy? How would they be kept in a constant orbit? Hence, the limitation of the simple model would be that the atom would decay quickly, as electrons would spiral into the nucleus. In other words, the simple model cannot explain why matter is stable.

7.1.4 Outline evidence for the existence of atomic energy levels

Elements emit light when given enough energy. This light can be analysed and each element has its own spectra. This is because elements do not provide a continuous spectrum of light.

Emission Spectra and absorption spectra

Line spectra is produced when the element radiates light. This spectra corresponds to wavelengths of the same energy level jump, hence, different elements have different spectra. Elements can only occupy given energy levels and is said to be quantised. When the electron moves between the energy levels, it emits or absorbs energy.This energy is emitted or absorbed as "packets" of light called photons. When the electron emits energy in an emission spectra, it gives it off as a wavelength of light of a particular colour. When the electron absorbs energy in an absorption spectra, the light of the particular wavelength is shown as a black line.

Photons

Light is not simply a continuous wave but is emitted as "packets" of light called photons. Only photons of the same energy as the energy in the electron jump will be emitted.

$E=hf$

Whereby:

E= photon energy (J)

h= Planck's constant (6.63*10^{-34} Js)

f= Frequency of light (Hz)

Nuclear structure

7.1.5 Explain the terms nuclide, isotope and nucleon.

Word	Definition
Nuclide	A particular species of atom which contains a specific number of protons and neutrons.
Isotope	Atoms that contain the same number of protons but different number of neutrons
Nucleon	The protons and neutrons in the nucleus

7.1.6 Define nucleon number (A), proton number (P) and neutron number (N)

Word	Definition
Nucleon number	The number of nucleons (protons and neutrons)
Atomic/proton number	The number of protons in the nucleus
Neutron number	The number of neutrons in an atom N=A-P

7.1.7 Describe the interactions in a nucleus

There are forces that exist within the nucleus of the atom.

Force (interaction)	Description
Gravitational force	This is the attractive force that exists between the masses of the protons and the neutrons. It is a comparatively weak force.
Electrical force	The positive charges of the protons in a nucleus create a repulsive force that is comparatively strong to the gravitational forces of attraction.
Strong nuclear force	Stronger than the repulsive electrical force, the attractive strong force keeps the protons from flying out of the nucleus. This force has an incredibly short range and is dependent on neutrons.

7.2 Radioactive decay

Radioactivity

7.2.1 Describe the phenomenon of natural radioactive decay

Radioactive decay is basically atoms (or more specifically nuclei) spontaneously breaking off small parts (alpha, beta and gamma particles) of themselves. This was accidentally discovered due to the effects of these particles on photographic film which was being kept in a drawer with them.

This lead to a systematic analysis of such particles, and the elements which produced them. The three different types mentioned above were found and separated, and the effect on the atoms undergoing this process (changing elements from one type to another) was examined.

7.2.2 Describe the properties of alpha (α) and beta (β) particles and gamma (γ) radiation

The three types of radiation were first divided by their ionising power. Rutherford later showed an alpha particle to be the nucleus of a helium atom by measuring their emission spectra. Beta particles were found to be free electrons, but emitted from the nucleus as a result of the changes which occurred in it. Gamma rays were found to be a type of very high frequency electromagnetic radiation.

7.2.3 Describe the ionizing properties of alpha (α) and beta (β) particles and gamma (γ) radiation

The products of alpha and beta decay are quite easy to find. Simply write out and balance the nuclear equations.

^A_ZX -> ^A-4_Z-2Y + ⁴₂He. The specific isotope represented by Y can then be determined.

7.2.4 Outline the biological effects of ionizing radiation

Radiation tends to ionise (strip the electrons from) gases when it passes through. This fact is used for the detection of radiation with Geiger counters. (No real detailed knowledge is required here.)

7.2.5 Explain why some nuclei are stable while others are unstable

The larger the ratio of neutrons to protons in a nucleus, the more stable a nuclei will be. This is due to the fact that the strong force caused by the neutrons (and the protons) will out weigh the repulsive electrostatic force cause be the positive protons. Also, increasing the distance between protons by having neutrons in between them will also reduce the electrostatic forces experienced by the protons further stabilizing the nucleus. Nuclei with a high number or neutrons to protons will there for be stable while nuclei with a low number of neutrons to protons will be unstable

Half-life

7.2.6 State that radioactive decay is a random and spontaneous process and that the rate of decay decreases exponentially with time

Artificial transmutation : When atoms decay, they change into different atoms, and this is called artificial transmutation. Atoms usually only lose alpha and beta particles (gamma is just a loss of energy, so not relevant here). An alpha particle is 2 protons and 2 neutrons. A beta particle is 1 negative charge, which turns a neutron into a proton in the nucleus. These facts can be put together to predict the results of nuclear equations. Transmuation also occurs when atoms of one element change into atoms of another element during fusion reactions, or during bombardment of an element with alpha particles or other small nuclear particles. An example is the bombardment of uranium by deturions to create plutonium.

Describe how the reaction between N and He led to the discovery of the proton : By bombarding nitrogen nuclei with alpha particles, Rutherford caused the ejection of hydrogen nuclei and the production of a new oxygen nucleus. As a result, the proton was discovered.

7.2.7 Define the term radioactive half‑life

Half life is the period of time (average, though accurate for a large number of atoms) required for the rate of decay of a radioactive sample to decrease to half its initial value. This is a constant for a given isotope.

7.2.8 Determine the half-life of a nuclide from a decay curve

The reactivity after n half lives will be Initial x (¹/₂)ⁿ. This equation is not in the data booklet, but is hopefully fairly obvious.

7.2.9 Solve radioactive decay problems involving integral numbers of half-lives

Radioactive decay is a random process for individual atoms, but overall, a block of radioactive atoms' rate of decay is exponential, falling to zero eventually. The decay rate can not be affected by physical or chemical conditions. For a large number of atoms, the number of radioactive atoms will halve over a regular period of time, called the half life, and this results in the exponential nature.

The half life life can be determined from a graph by first taking a point on the graph, finding its rate of decay. Calculate the rate of decay which is half of the original value, then find the point on the graph which corresponds to this half rate. The half life is the time (from the x-axis) between the two points.

Nuclear reactions

7.3.3 Define the term unified atomic mass unit

The unified atomic mass unit is the mass of one-twelfth of the nucleus of a carbon-12 isotope

7.3.4 Apply the Einstein mass–energy equivalence relationship

$E=mc^{2}$

Extra stuff

The idea of Millikan's oil drop experiment was to have very small oil drops which had some charge balanced between two electric plates. By knowing the strength of the field between the plates, it was possible to calculate the amount of force being applied per charge on the drop, which, if it was floating, would be exactly the same as the force of gravity downwards. From this, it is possible to find the mass to charge ratio of the drops.

The mass of the drop was then measured by cutting the field and measuring its terminal velocity and using stokes equation. This allowed the charges on the drops to be found, and it was found that the smallest difference between these charges was 1.6 × 10^-19 C, the charge of a single electron.

If a mass is being suspended by an electric field, then mg = qE (mass × gravity = charge × electric field strength). Electric field strength can be can be expressed as ^V/_d (potential difference divided by distance), for calculation purposes. The results showed that the minimum difference between charges was 1.6 × 10^-19 C and so this must be the smallest unit of charge possible. This means that charge must be quantized (only comes in discrete chunks rather than being continuous), and the quantum of charge was 1.6 × 10^-19 C. An electron gun relies on the principle of thermonic emission. There is a large PD created between two metal plates in a vacuum. The cathode (the negative one from which the electrons come) emits a bunch of electrons. They accelerate towards the anode (the positive plate), which has a hole in it, and so some of the electrons fly through and create a sort of beam of electrons (originally called a cathode ray).

Cathode rays can be deflected by both electric and magnetic fields, and act as negatively charged particles would in such fields. Both these properties can be explained by the fact that they are actually electrons.

Thompson's experiment involved using electric and magnetic fields to exactly cancel each other's effects and allow an electron to pass undeflected. The electric field is then removed and the radius of curvature is measured. The equations then simplify down to give an expression for ^e/_m in which all the other terms are known, and so the ratio of charge to mass could be accurately found.

By knowing the charge of an electron (Millikan) and the charge to mass ratio (Thompson) it is possible to find the mass of an electron. That makes Thompson the discoverer of the electron (hooray for him).