Radioactivity and Nuclear Equations

To understand nuclear reactions, we must review and develop some ideas introduced in Section 2.3. First, recall that two types of subatomic particles reside in the nucleus protons and neutrons. We will refer to these particles as nucleons. Recall also that all 

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RADIOACTIVITY AND NUCLEAR EQUATIONS We begin by learning how to describe nuclear reactions using equations analogous to chemical equations, in which the nuclear charges and masses of reactants and products are in balance. We see that radioactive nuclei most commonly decay by emission of alpha, beta, or gamma radiation. 

In order to describe radioactive transformations, nuclear equations are needed. These are very similar to chemical equations, except that the nucleon numbers and proton numbers of each reactant must also be specified, that is, the reactions are written with nuclides. A typical nuclear equation, representing the decay of an isotope of uranium, uranium-238, is ... 

Chapter 5, Nuclear Chemistry, looks at the types of radiation emitted from the nuclei of radioactive atoms. Nuclear equations are written and balanced for both naturally occurring radioactivity and artificially produced radioactivity. The half-lives of radioisotopes are discussed, and the amount of time for a sample to decay is calculated. Radioisotopes important in the field of nuclear medicine are described. 

Nuclear chemistry nuclear equations, half-lives, and radioactivity chemical applications... 

Write the nuclear equation for the radioactive decay of potassium-40 by beta emission. Identify the parent and daughter nuclides in the decay. 

Thorium-234 is also radioactive. When it decays, it emits a beta particle. Recall that a beta particle is an electron emitted by a neutron as the neutron transforms to a proton. So with thorium, which has 90 protons, beta emission leaves the nucleus with one fewer neutron and one more proton. The new nucleus has 91 protons and is no longer thorium now it is the element protactinium. Although the atomic number has increased by 1 in this process, the mass number (protons + neutrons) remains the same. The nuclear equation is... 

Neptunium-237 undergoes an a, p, a, a, p, a, a, a, p, a, p sequence of radioactive decays. Determine the daughter nuclide after each decay and write a balanced nuclear equation for each step. 

Note how the nuclear equation for the radioactive decay of uranium-238 is written. The equation is not balanced in the usual chemical sense because the kinds of nuclei are not the same on both sides of the arrow. Instead, a nuclear equation is balanced when the sums of the nucleons are the same on both sides of the equation and when the sums of the charges on the nuclei and any elementary particles (protons, neutrons, and electrons) are the same on both sides. In the decay of 2 U to give He and 2 oTh, for example, there are 238 nucleons and 92 nuclear charges on both sides of the nuclear equation. 

In some radioactive decays, one proton is transformed into one neutron and a positively charged particle with the same mass as a beta 0") particle (or electron) is produced. Emission of this positively charged particle is known as positron emission. Positrons (antielectrons) are symbolized as P+ or e. The nuclear equation of the formation of a positron particle is i . i . o ... 

QM grew out of studies of blackbody radiation and of the photoelectric effect. Besides QM, radioactivity and relativity contributed to the transition from classical to modem physics. The classical Rutherford nuclear atom, the Bohr atom, and the Schrodinger wave-mechanical atom are discussed. Hybridization, wavefunctions, Slater determinants and other basic concepts are explained. For obtaining eigenvectors and eigenvalues from the secular equations the elegant and simple matrix diagonalization method is explained and used. All the necessary mathematics is explained. 

The AP test requires you to know about nuclear equations, half-lives, radioactivity, and chemical applications of nuclear properties. This chapter begins with a brief review of the history of the nucleus and how we came to know about it and then moves into the required topics. 

A) Identify the type of radioactive decay that oxygen-14 will undergo, and write a balanced nuclear equation for the process. 

Tritium is hydrogen of mass number 3, having two neutrons and a proton in its nucleus. It is radioactive (half-life 12.4 years) in common with many isotopes having a large neutron-to-proton ratio, tritium decays with emission of an electron (called a beta ray). Such a decay can be represented by the nuclear equation (see also Chap. 27) ... 

Note that in equation (10), as in the other nuclear equations listed, atomic numbers and mass numbers are both conserved. This reaction was the first artificial transmutation, carried out (as contrasted to spontaneous transmutations or natural radioactivity in which one nucleus is transformed to another, irrespective of the influence of man). The a particle in equation (10) is the projectile and the nitrogen nucleus the target. 

Equations (5.7) and (5.8) are known as Carnot s equations. In Eq. (5.7) the smallest possible value of QC is zero the corresponding value of Tc is the absolute zero of temperature on the Kelvin scale. As mentioned in Sec. 1.4, this occurs at -273.15°C. Equation (5.8) shows that the thermal efficiency of a Carnot engine can approach unity only when TH approaches infinity or Tc approaches zero. On earth nature provides heat reservoirs at neither of these conditions all heat engines therefore operate at thermal efficiencies less than unity. The cold reservoirs naturally available are the atmosphere, lakes and rivers, and the oceans, for which Tc = 300 K. Practical hot reservoirs are objects such as furnaces maintained at high temperature by combustion of fossil fuels and nuclear reactors held at high temperature by fission of radioactive elements, for which T = 600 K. With these values,... 

Types of Radioactive Decay and Balancing Nuclear Equations... 

There are three main types of radioactive decay alpha particle emission, beta particle emission, and the emission of gamma radiation. When an unstable isotope undergoes radioactive decay, it produces one or more different isotopes. We represent radioactive decay using a nuclear equation. Two rules for balancing nuclear equations are given below. 

Just as we did for natural radioactive reactions we can balance nuclear equations for artificial reactions by making the superscripts on the left and right sides add up to the same quantity, and also the subscripts. 

Now Tm going to tell you about a strange concept that s necessary for understanding radioactivity and other nuclear reactions. That concept is the equivalence of mass and energy. Mass can transform into energy, and vice versa. This is part of Einstein s theory of special relativity and is the source of that famous equation E = m. Let s apply the theory to the activities you did in the previous section. When the two magnets are apart, we say that they have potential energy due to... 

Predict the particles and electromagnetic waves produced by different types of radioactive decay, and write equations for nuclear decays. 

The radioactive decay processes you have just read about are all examples of nuclear reactions. As you probably noticed, nuclear reactions are expressed by balanced nuclear equations just as chemical reactions are expressed by balanced chemical equations. However, in balanced chemical equations, numbers and kinds of atoms are conserved in balanced nuclear equations, mass numbers and atomic numbers are conserved. 

When you write nuclear equations, it is important to indicate which isotopes of the given elements you are dealing with. For example, the element carbon has natural isotopes with three different atomic masses carbon-12, carbon-13, and carbon-14. Two of these, carbon-12 and carbon-13, are stable isotopes and are not radioactive. However, carbon-14 is unstable and radioactive. There must be some way to distinguish between these isotopes in nuclear equations. To do this, you write the mass number as a superscript and atomic number as a subscript in the symbol for an isotope. These numbers are both placed to the left of the symbol for the element. So, the three isotopes of carbon are represented as C, C, and... 

Write the balanced nuclear equation for the radioactive decay of radium-226 to give radon-222, and determine the type of decay. 

Compare and contrast nuclear fission and nuclear fusion. Demonstrate equations that represent the changes that occur during radioactive decay. 

In nuclear equations for alpha emission, the alpha particle is written as either a or 2He. Note that in alpha emission, the radioactive nuclide changes into a different element, with an atomic number that is lower by 2 and a mass number that is lower by 4. 

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