Conceptual Physics

As far as high-energy physicists are concerned, the goal is a Grand Unification Theory, or GUT. The current dream is to unify gravity with the

strong, weak, and electromagnetic forces. You may have heard of attempts such as superstring theory, which interpret particles, such as

electrons, as being modes of oscillation of unimaginably small “strings”. Acceptance of superstring theory demands the idea that the universe

may not consist of four dimensions (three spatial dimensions plus time), but instead ten or more dimensions. Bizarre as these ideas may seem,

they are no less bizarre than relativity, nuclear theory, and quantum physics would have seemed to a scientist of the 19th century.

38.20 - Gotchas

All carbon atoms are the same. Not true: While carbon atoms all have six protons in their nucleus, different carbon atoms may have different

numbers of neutrons. Nuclei with six protons but different numbers of neutrons are isotopes of carbon.

The nucleus is so small that an atom is about 99.99% empty space. No, but you are on the right track if you think this. Since the atomic

diameter is about 10,000 times larger than the nucleus, the atom is more like 99.9999999999% empty space.

Protons and neutrons have different charge but approximately the same mass. Yes. A proton has a charge of 1.60×10í^19 C and a neutron has

no net electrical charge. The neutron is about 0.1% more massive than the proton, and they are each about 1800 times as massive as the

electron.

The energy that is required to disassemble a nucleus into its constituent parts is the same amount of energy that is released when the same

nucleus is assembled from separated nucleons. Yes; the amount of energy is the same and is called the binding energy. It requires energy to

break apart a stable nucleus, and energy is released when the nucleus is assembled.

If half of a radioactive isotope decays during one half-life, then after two half-lives, it will all be gone. No, a half-life is the average time it takes

for one-half of the radioactive material that is present to decay. After two half-lives, there will be one-quarter of the original amount left. After

three half-lives, there will be one-eighth, and so on.

38.21 - Summary

Elements are substances that cannot be divided or changed into other substances

using ordinary chemical methods. An atom is the smallest piece of an element that

still has its chemical and physical properties. An atom consists of electrons orbiting

a very small, very dense nucleus. The nucleus contains both protons and neutrons,

which collectively are called nucleons.

The number of protons in an atom is the atomic number, Z. The number of neutrons

is the neutron number, N. The total is known as the atomic mass number, A. Atomic

masses are measured in terms of atomic mass units. The mass of a carbon-12

atom is defined to be exactly 12 u.

Isotopes are forms of an element with the same atomic number (which makes them

the same element) but different numbers of neutrons (and hence different atomic

mass numbers).

A fundamental, very short-range interaction called the strong force holds the

nucleons together, counteracting the electrostatic repulsion between protons.

The nucleons are nearly incompressible and are tightly packed in the nucleus. The

nuclear radius grows roughly as the cube root of the mass number.

Nuclei are stable only for certain combinations of protons and neutrons. On a plot of

neutron number versus proton number, stable nuclei are represented as a band of

stability that passes through the center of the diagram. For small nuclei, the

numbers of protons and neutrons are roughly equal, but for large nuclei, the

neutrons outnumber the protons by about 50%. Heavy nuclei need an excess of neutrons to dilute the proton concentration.

Binding energy is the energy that must be added to disassemble, or unbind, a nucleus into the protons and neutrons that make it up. The same

amount of energy is released if the nucleus is assembled from nucleons that are initially separated.

The sum of the masses of the separate nucleons is always greater than the mass of the nucleus when it is whole. The mass difference is

related to the binding energy by Einstein’s equation for mass-energy equivalence.

When the binding energy of one nucleus is greater than that of another, this means the particles are more tightly bound. For comparing how

tightly bound two nuclei are, the binding energy per nucleon is the important figure.

The shape of the binding energy per nucleon vs. mass number curve is important. The curve is highest in the middle. This means that light

nuclei can undergo the fusion process and release energy as this will increase their binding energy per nucleon. Similarly, heavy nuclei can

undergo the fission process and release energy as this also will increase their binding energy per nucleon.

In the process of radioactive decay, an unstable nucleus spontaneously emits particles or high-energy photons. If the parent nucleus emits a

charged particle such as an Į particle, negative ȕ, or positive ȕ, then the number of protons in the nucleus changes. Transmutation is the

changing of one element to another. If the parent nucleus emits gamma rays, which are uncharged photons, then transmutation does not take

place, because the number of protons in the nucleus has not changed.

The half-life of a radioactive isotope is the average time it takes for the decay of one-half of the atoms that are present in a sample.

Z = atomic (proton) number

N = number of neutrons

Atomic mass number

A = Z + N

Atomic mass unit

u = 1.66054×10–27 kg

Nuclear radius

R = (1.2×10–15 m)A1/3

Mass-energy equivalence

E = mc^2

(^716) Copyright 2007 Kinetic Books Co. Chapter 38