Lecture 38, Dec. 11, 2000

Announcements:

The problems from chapter 30 can be omitted. They will not be used on the final exam.
For the final exam, you are expected to know the values of the metric prefixes from pico (10^-12) to Giga (10⁹). These will not be given on the equation sheet.

Recall from last lecture:

Nuclei are composed of neutrons and protons.
A nucleus of element X with Z protons, N neutrons, and A = Z + N neutrons is indicated as ^A_ZX.
E_bind = (Z m_p + N M_n - M_nucleus)c².

29.4 The Decay Process

When a nucleus decays, it is transformed in some way. This transformation is called the decay process, and is indicated by a decay formula such as X --> Y + Z. As in chemistry, there are rules for valid formulas:

Charge is conserved in a decay process.
The number of nucleons (the mass number) is conserved.

Let's look at how these apply to each of the three decay types.

Alpha Decay

In alpha decay the original nucleus (called the parent nucleus) breaks up into a decay nucleus (called the daughter) and a ⁴₂He nucleus. Since charge and the number of nucleons are both conserved, if the parent nucleus is ^A_ZX, then the daughter nucleus is ^A-4_Z-2Y, where X is the element with atomic number Z, and Y is the element with atomic number Z-2.

Beta Decay

In beta decay, a neutron in the parent nucleus convertes into a proton, an electron, and a third particle called an anti-neutrino. The anti-neutrino, written as the greek letter nu with a bar over top (nubar), is neutral, massless, and very hard to detect, but its presence is evident from the range of electron energy in the decay. Here charge is conserved, since the proton and electron charge in the final state ad up to zero. In beta decay, the daughter nucleus has the same mass number, A, as the parent, but the atomic number increases by 1. An example beta decay formula is written:
^A_ZX --> ^A_Z+1X + e^- + nubar

Gamma Decay

Gamma decay occurs when a nucleus in an excited state decays to a lower state, and emits a gamma ray. In gamma decay the number of protons, and neutrons is unchanged.

Example: P29.24

Complete the following radioactive decay formulas:
¹²₅B --> ? + e^- + nubar
²³⁴₉₀Th --> ²³⁰₈₈Ra + ?
? --> ¹⁴₇N + e^- + nubar

The first decay is clearly a beta decay. A neutron in the parent nucleus is transformed into a proton (which remains in the daughter nucleus), an electron, and an anti-neutrino. Therefore, the daughter nucleus has the same number of nucleons as the parent, but one less neutron and one more proton, for a total of 6 protons. Therefore, the daughter nucleus is carbon:
¹²₅B --> ¹²₆C + e^- + nubar

The second decay is an alpha decay since the resulting nucleus has 4 fewer nucleons and 2 fewer protons than the parent nucleus. This decay is:
²³⁴₉₀Th --> ²³⁰₈₈Ra + ⁴₂He

The third decay is a beta decay. The parent nucleus will have one less proton and one additional neutron than the daughter nucleus. Therefore the parent nucleus has 6 protons and is carbon:
¹⁴₆C --> ¹⁴₇N + e^- + nubar

29.5 Natural Radioactivity

omit from lecture

29.6 Nuclear Reactions

Nuclear reactions occur when two nuclei collide. Rutherford first did this in the laboratory in a variation of the famous scattering experiment. He collided alpha particles with nitrogen nuclei, observing an outgoing hydrogen:

⁴₂He + ¹⁴₇N --> X + ¹₁H

To determine the nature of X, we balance the neutrons and protons on both sides. The left side of the reaction has 9 protons and 9 neutrons. The right side must have as many, therefore X must have 8 protons and 9 neutrons, since hydrogen has but 1 proton. The element with 8 protons is oxygen, therefore X is ¹⁷₈O.