Premed · Premed · General Chemistry 2
Lecture 17: Nuclear Chemistry: Radioactivity
General Chemistry II
Learning Objectives
By the end of this lecture, students will be able to:
- Compare and contrast chemical reactions with nuclear reactions
- Describe the types of radioactive decay (alpha, beta, gamma, positron emission, electron capture)
- Write balanced nuclear equations
- Explain the band of stability and predict the mode of decay for unstable nuclei
- Define and calculate half-life for radioactive decay (first-order kinetics)
- Describe methods of detecting radiation and units of radioactivity
Lecture Content
I. Nuclear Reactions vs. Chemical Reactions
Nuclear reactions differ from chemical reactions in several fundamental ways. Chemical reactions involve the rearrangement of valence electrons, leaving atoms unchanged as elements. Nuclear reactions involve changes to protons and neutrons within the nucleus and can transform one element into another entirely. The energy changes in nuclear reactions are roughly a million times larger than in chemical reactions. While chemical reaction rates are influenced by temperature, concentration, and catalysts, nuclear decay rates are essentially unaffected by any external conditions.
Several terms are essential for discussing nuclear chemistry. A nucleon is a proton or neutron. A nuclide is a specific nuclear species characterized by its atomic number Z (number of protons) and mass number A (total number of protons and neutrons). Isotopes are nuclides of the same element (same Z) that differ in mass number (different neutron count). Nuclear species are denoted using the notation ^A_Z X, such as ^14_6 C for carbon-14.
II. Types of Radioactive Decay
Alpha decay involves the emission of an alpha particle, which is a helium-4 nucleus (^4_2 He). This mode of decay is characteristic of heavy nuclei with Z greater than 83. The mass number decreases by 4 and the atomic number decreases by 2. For example, ^238_92 U -> ^234_90 Th + ^4_2 He. Alpha particles have low penetrating power (stopped by a sheet of paper) but high ionizing power.
Beta decay involves the emission of a beta particle, which is an electron (^0_(-1) e) produced when a neutron converts to a proton within the nucleus: n -> p + e-. The mass number remains unchanged while the atomic number increases by 1. Carbon-14 undergoes beta decay: ^14_6 C -> ^14_7 N + ^0_(-1) e. This decay mode occurs when the neutron-to-proton ratio is too high.
Positron emission involves the emission of a positron (^0_(+1) e), the antimatter counterpart of the electron, produced when a proton converts to a neutron: p -> n + e+. The mass number remains unchanged while the atomic number decreases by 1. For instance, ^11_6 C -> ^11_5 B + ^0_(+1) e. This occurs when the neutron-to-proton ratio is too low.
Electron capture is a competing process in which the nucleus captures an inner-shell electron, converting a proton to a neutron: p + e- -> n. The result is the same as positron emission: unchanged mass number and atomic number decreased by 1. An example is ^55_26 Fe + ^0_(-1) e -> ^55_25 Mn.
Gamma emission involves high-energy electromagnetic radiation emitted from an excited nucleus. Because gamma rays carry no mass and no charge, neither the mass number nor the atomic number changes. Gamma emission usually accompanies other types of decay. Gamma rays have the highest penetrating power of all radiation types, requiring lead or thick concrete for shielding.
<image>A diagram comparing the three main types of radiation. Panel A: Alpha particle (large, positive, shown as a helium nucleus) blocked by a sheet of paper. Panel B: Beta particle (small, negative, shown as an electron) passes through paper but blocked by a thin sheet of aluminum. Panel C: Gamma ray (wavy line, no charge) passes through paper and aluminum but partially blocked by thick lead or concrete. A table below compares: charge (+2, -1, 0), mass (4 amu, ~0 amu, 0), penetrating power (low, medium, high), ionizing power (high, medium, low), and notation for each type.</image>
III. Balancing Nuclear Equations
Balancing nuclear equations requires conserving both mass number (A) and atomic number (Z). The sum of mass numbers on the left must equal the sum on the right, and likewise for atomic numbers. To identify an unknown particle, determine what values of A and Z are needed to balance the equation.
For example, in ^241_95 Am -> ^237_93 Np + ?, the unknown must have A = 241 - 237 = 4 and Z = 95 - 93 = 2, identifying it as ^4_2 He, confirming alpha decay.
IV. The Band of Stability
The band of stability is a region on a graph of neutron number versus proton number where stable nuclei exist. For light nuclei with Z less than 20, the stable neutron-to-proton ratio is approximately 1:1. For heavier nuclei, the ratio increases because additional neutrons are needed to offset the growing electrostatic repulsion among protons. By Z = 82 (lead), the stable n/p ratio has risen to approximately 1.5:1.
The position of an unstable nucleus relative to the band of stability predicts its decay mode. Nuclei above the band (too many neutrons) undergo beta decay, which converts a neutron to a proton and decreases the n/p ratio. Nuclei below the band (too many protons) undergo positron emission or electron capture, both of which convert a proton to a neutron and increase the n/p ratio. Nuclei with Z greater than 83 undergo alpha decay to reduce both Z and A.
Magic numbers of protons or neutrons (2, 8, 20, 28, 50, 82, and 126) confer exceptional stability, analogous to the noble gas electron configurations. Nuclei with even numbers of both protons and neutrons also enjoy extra stability.
<image>A graph of number of neutrons (N, y-axis) vs. number of protons (Z, x-axis) showing the band of stability. Stable nuclides are plotted as dots forming a band. A diagonal line represents N = Z (the 1:1 ratio). For light elements, the band follows this line. For heavier elements, the band curves above the line (more neutrons than protons). The region above the band is labeled "Beta decay (n/p too high)" with an arrow pointing toward the band. The region below is labeled "Positron emission or electron capture (n/p too low)" with an arrow. Beyond Z = 83, all nuclei are labeled "Unstable -- alpha decay." Magic numbers are marked with dashed lines at Z or N = 2, 8, 20, 28, 50, 82, 126.</image>
V. Radioactive Decay Kinetics
Radioactive decay follows first-order kinetics, governed by the equation N = N_0 e^(-lambda t), where lambda is the decay constant and N is the number of radioactive atoms remaining at time t. The logarithmic form is ln(N/N_0) = -lambda t. The rate of decay is Rate = lambda N.
The half-life is related to the decay constant by t_(1/2) = 0.693 / lambda. After n half-lives, the number of atoms remaining is N = N_0 (1/2)^n. Activity, defined as the number of disintegrations per unit time, is given by A = lambda N and follows the same exponential decay: A = A_0 e^(-lambda t). Activity is measured in becquerels (Bq), where 1 Bq = 1 disintegration per second, or in curies (Ci), where 1 Ci = 3.7 x 10^10 disintegrations per second.
Half-lives span an extraordinary range: ^214_84 Po has a half-life of just 1.6 x 10^-4 seconds, ^14_6 C has a half-life of 5,730 years, and ^238_92 U has a half-life of 4.5 x 10^9 years.
VI. Radiometric Dating
Carbon-14 dating exploits the fact that ^14C is continually produced in the upper atmosphere by cosmic ray bombardment of ^14N. Living organisms maintain a constant ratio of ^14C to ^12C through metabolic exchange with the environment. Upon death, ^14C decays without replenishment, so measuring the remaining ^14C/^12C ratio (or residual activity) reveals the time since death. The method is effective for samples up to approximately 50,000 years old, corresponding to about 9 half-lives of carbon-14.
Uranium-lead dating uses the decay of ^238U to ^206Pb (with a half-life of 4.5 x 10^9 years) to date geological samples. The ratio of ^206Pb to ^238U in a mineral indicates the time since the mineral crystallized. This method has been instrumental in determining the age of the Earth.
VII. Detection and Measurement of Radiation
Several instruments detect and measure radiation. The Geiger-Muller counter detects ionizing radiation by measuring electrical pulses generated when radiation ionizes gas molecules inside a tube. Scintillation counters use a phosphor material that produces flashes of light when struck by radiation; a photomultiplier counts these flashes. Film badges, worn by radiation workers, contain photographic film that darkens in proportion to radiation exposure.
Radiation dosimetry uses specific units to quantify exposure. The absorbed dose is measured in grays (1 Gy = 1 J/kg) or rads (1 rad = 0.01 Gy). The dose equivalent, which accounts for the varying biological effectiveness of different radiation types, is measured in sieverts (Sv = Gy x quality factor) or rems (rem = rad x quality factor). Quality factors differ by radiation type: gamma and beta radiation have a factor of 1, while alpha particles have a factor of 20 and neutrons range from 5 to 20, reflecting their greater biological damage per unit of absorbed energy. The average annual background radiation dose is approximately 3.6 mSv (360 mrem).
