Nuclear Chemistry

Nuclear Chemistry {21.1-Radioactivity

The Nucleus • Remember that the nucleus is composed of the two nucleons, protons and neutrons. • The number of protons is the atomic number. • The number of protons and neutrons together is effectively the mass of the atom.

Isotopes • Not all atoms of the same element have the same mass, due to different numbers of neutrons in those atoms. • There are, for example, three naturally occurring isotopes of uranium: Uranium-234 Uranium-235 Uranium-238 • Nuclide-nucleus containing a specified number of protons and neutrons

Radioactivity • It is not uncommon for some nuclides of an element to be unstable, or radioactive. • We refer to these as radionuclides. • Atoms containing these nuclei are referred to as radioisotopes. • There are several ways radionuclides can decay into a different nuclide.

Radioactive decay • Radionuclides are unstable and spontaneously emit particles and electromagnetic radiation to transform into a more stable nuclide that has less energy • emitted radiation carries the excess energy Radioactive decay-spontaneous decomposition of an unstable nucleus

Nuclear Equations • Radioactive decay reactions are represented with nuclear equations • Mass numbers and atomic numbers must be balanced in all nuclear equations • Since radioactive properties of nuclei are independent of their chemical state, the chemical form of the atom in which the nucleus exists is not important

234 90 238 92 4 2 4 2 He U He Th +  Types of Radioactive Decay ALPHA DECAY • Alpha decay is the loss of an α-particle (a helium nucleus)

131 53 131 54 0 1 0 1 0 1 e I Xe e  +  or Types of Radioactive Decay BETA DECAY • Beta decay is the loss of a -particle (a high-energy electron)

11 6 11 5 0 1 0 1 e C B e +  Types of Radioactive Decay POSITRON EMISSION • Some nuclei decay by emitting a positron, a particle that has the same mass as, but an opposite charge to, that of an electron

0 0  Types of Radioactive Decay GAMMA EMISSION • Gamma emission is the loss of a -ray, which is high-energy radiation that almost always accompanies the loss of a nuclear particle

0 1 1 1 1 0 p e n +  Types of Radioactive Decay ELECTRON CAPTURE (K-CAPTURE) • Addition of an electron to a proton in the nucleus is known as electron capture or K-capture. • The result of this process is that a proton is transformed into a neutron:

Radioactive Decay

Concept Check 21.1 Predicting the Product of a Nuclear Reaction PROBLEM 21.1a: What product is formed when radium-226 undergoes alpha decay? Answer: 226 = A + 4 , A = 222 88 = Z + 2 , Z = 86 The element with atomic number 86 is radon, Rn, therefore

Concept Check 21.1 Predicting the Product of a Nuclear Reaction PROBLEM 21.1b: Which element undergoes alpha decay to form lead-208? Answer:

Concept Check 21.2 Writing Nuclear Equations PROBLEM 21.2a: Write a nuclear equation for mercury-201 undergoing electron capture. Answer: 201 + 0 = A , A = 201 80 - 1 = Z , Z = 79 The element with atomic number 79 is gold, Au, therefore

Concept Check 21.2 Predicting the Product of a Nuclear Reaction PROBLEM 21.2b: Write nuclear equations for (i)thorium-231 decaying to protactinium-231; (ii) oxygen-15 undergoes positron emission. Answer: (i) (ii)

Nuclear Chemistry {21.2-Patterns of Nuclear Stability

Predicting Stability of Nuclei • Although there is no single rule to predicting the stability of a nucleus, several empirical observations can help: • Neutron-to-proton ratio • Radioactive series • Magic numbers • Even vs. odd nucleons

Neutron-to-Proton Ratios • Any element with more than one proton (i.e., anything but hydrogen) will have repulsions between the protons in the nucleus • A strong nuclear force helps keep the nucleus from flying apart. • Neutrons play a key role stabilizing the nucleus. • Therefore, the ratio of neutrons to protons is an important factor.

Neutron-to-Proton Ratios • For small nuclei (Z< 20), stable nuclei have a neutron-to-proton ratio close to 1:1. • As nuclei get larger, it takes a larger number of neutrons to stabilize the nucleus. Thus, the neutron-to-proton ratio of stable nuclei increase with increasing atomic number

Neutron-to-Proton Ratios The shaded region in the figure, the so-called belt of stability, shows what nuclides would be stable.

Neutron-to-Proton Ratios • Nuclei above the belt have too many neutrons (HIGH n0-p+ ratio) • These nuclei tend to decay by emitting beta particles (dec #n0 and inc #p+)

Neutron-to-Proton Ratios • Nuclei below the belt have too many protons (LOW n0-p+ ratio) • These nuclei tend to become more stable by positron emission or electron capture (inc #n0 and dec #p+)

Neutron-to-Proton Ratios • There are no stable nuclei with an atomic number greater than 83. • Nuclei with such large atomic numbers tend to decay by alpha emission (dec both #n0 and #p+)

Neutron-to-Proton Ratios • Keep in mind that the belt of stability guidelines do not always work. For example, thorium-233, which we might expect to undergo alpha decay, actually undergoes beta emission. Furthermore, few radioactive nuclei lie within the belt of stability. Both neodynmium-146 and neodymium-148, for example, are stable and lie in the belt of stability. Neodymium-147, however, which lies between them, is radioactive.

Radioactive Decay Series • Large radioactive nuclei cannot stabilize by undergoing only one nuclear transformation. • They undergo a series of decays until they form a stable nuclide (often a nuclide of lead).

Magic Numbers • Nuclei with 2, 8, 20, 28, 50, or 82 protons or 2, 8, 20, 28, 50, 82, or 126 neutrons tend to be more stable than nuclides with a different number of nucleons.

Even vs. Odd Nucleons • Nuclei with an even number of protons and neutrons tend to be more stable than nuclides that have odd numbers of these nucleons.

Concept Check 21.4 Predicting Nuclear Stability PROBLEM 21.4a: Predict which of these nuclei are especially stable: Answer: We are asked to identify especially stable nuclei, given their mass numbers and atomic numbers, therefore we must look to see whether the numbers of protons and neutrons correspond to magic numbers and even/odd characteristics of their nucleons. Has a magic number of both protons (2) and neutrons (2) and is therefore especially stable. Has a magic number of both protons (20) and neutrons (20) and is therefore especially stable. Does not have a magic number of either protons or neutrons, and also has an odd number of both protons (43) and neutrons (55). This nucleus is not stable.

Concept Check 21.4 Predicting Nuclear Stability PROBLEM 21.4b: Predict which of these nuclei are especially stable: Answer:

Nuclear Chemistry {21.3 Nuclear Transmutations

Bombardment Reactions • A nucleus can also undergo transformation by accelerating a particle and colliding it with the nuclide. • These bombardment reactions have allowed for the laboratory synthesis of hundreds of radioisotopes.

Bombardment Reactions • These nuclear transmutations are often represented by listing, in order, the target nucleus, the bombarding particle, the ejected particle, and the product nucleus.

Particle Accelerators • To overcome the electrostatic repulsion between the target nucleus and a bombarding particle (like an alpha particle), the bombarding particle must be accelerated through the use of strong magnets and electrostatic fields. • “Atoms smashers” include cyclotrons and synchrotrons.

Particle Accelerators • Particle accelerators are enormous, having circular tracks with radii that are miles long.

Concept Check 21.5 Writing a Balanced Nuclear Equation PROBLEM 21.5a: Write the balanced nuclear equation for the process summarized as . Answer: We must go from the condensed descriptive form of the reaction to the balanced nuclear equation. We arrive at the balanced equation by writing n and α, each with its associated subscripts and superscripts.

Concept Check 21.5 Predicting Nuclear Stability PROBLEM 21.5b: Write the condensed version of the nuclear reaction: Answer:

Nuclear Chemistry {21.4-Rates of Radioactive Decay

Half-life Different nuclei undergo radioactive decay at different rates. These rates are commonly expressed in terms of half-lives-time required for half of any given quantity of a substance to react Each isotope has its own characteristic half-life (ranging from millionths of a second to billions of years) Half-lives are unaffected by external conditions (temperature, pressure, state of chemical combination)

Concept Check 21.6 Calculation involving half-lives PROBLEM 21.6a: The half-life of cobalt-60 is 5.3 yr. How much of a 1.000-mg sample of cobalt-60 is left after 15.9 yr? Answer: We are given the half-life for cobalt-60 and asked to calculate the amount of cobalt-60 remaining from an initial 1.000-mg sample after 15.9 yr. We will use the fact that the amount of a radioactive substance decreases by 50% for every half-life that passes. Because 5.3 × 3 = 15.9, 15.9 yr is three half-lives for cobalt-60. At the end of one half-life, 0.500 mg of cobalt-60 remains, 0.250 mg at the end of two half-lives, and 0.125 mg at the end of three half-lives.

Concept Check 21.6 Calculation involving half-lives PROBLEM 21.6b: Carbon-11, used in medical imaging, has a half-life of 20.4 min. The carbon-11 nuclides are formed, and the carbon atoms are then incorporated into an appropriate compound. The resulting sample is injected into a patient, and the medical image is obtained. If the entire process takes five half-lives, what percentage of the original carbon-11 remains at this time? Answer: 3.12%

Radiometric Dating Since the half-life (t1/2) of a nuclide is constant, it can serve as a nuclear clock to determine the age of an object

Radiocarbon dating – carbon-14 isotope

Calculations Based on Half-life Radioactive decay is a first-order kinetic process (its rate depends on the concentration of a single reactant raised to the first power) The rate of radioactive decay is proportional to the number of radioactive nuclei (N) in a sample Rate = kN k = decay constant

Calculations Based on Half-life Activity-the rate at which a sample decays • Units of disintegrations per unit time • SI Unit: becquerel (Bq) = one disintegration per second • curie (Ci) = 3.7x1010disintegrations per second • As a sample decays, the amount of radiation emanating the sample decays as well

Nt N0 = - kt ln Calculations Based on Half-life A first order rate law can be expressed as t = time interval of decay N0= initial number of nuclei (at t = 0) Nt = number of nuclei remaining after a time interval, t k = decay constant

Calculations Based on Half-life IMPORTANT: The mass of an isotope and its activity are proportional to the number of radioactive nuclei Therefore, either the ratio of the mass at any time t to the mass at time t = 0, or the ratio of activities at time tand time t = 0, can be substituted in for Nt/N0

0.693 k t1/2= Calculations Based on Half-life Measurements of radioactive activity can also be used to determine the half-life of a radioisotope The half-life of nuclear transmutation can be determined k = decay constant

Nuclear Chemistry