Radioactive decay nuclear equations

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 ... 

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. 

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. 

The analysis of steady-state and transient reactor behavior requires the calculation of reaction rates of neutrons with various materials. If the number density of neutrons at a point is n and their characteristic speed is v, a flux effective area of a nucleus as a cross section O, and a target atom number density N, a macroscopic cross section E = Na can be defined, and the reaction rate per unit volume is R = 0S. This relation may be appHed to the processes of neutron scattering, absorption, and fission in balance equations lea ding to predictions of or to the determination of flux distribution. The consumption of nuclear fuels is governed by time-dependent differential equations analogous to those of Bateman for radioactive decay chains. The rate of change in number of atoms N owing to absorption is as follows ... 

Write the balanced nuclear equation for each of the following radioactive decays (a) p + decay of boron-8 (b) p decay of nickel-63 (c) a decay of gold-185 (d) electron capture by beryllium-7. 

Write the balanced nuclear equation for each of the following radioactive decays (a) p decay of uranium-233 ... 

Write balanced nuclear equations for the radioactive decay of each of the following nuclides (a) 4Kr, p+ emission ... 

Identify the daughter nuclides in each step of the radioactive decay of uranium-235, if the string of particle emissions is a, p, a, P, ct, a, a, P, a, p, a. Write a balanced nuclear equation for each step. 

The classic example of reactions of this type is a sequence of radioactive decay processes that result in nuclear transformations. The differential equations that govern kinetic systems of this type are most readily solved by working in terms of concentration derivatives. For the first reaction,... 

The basic concepts of nuclear structure and isotopes are explained Appendix 2. This section derives the mathematical equation for the rate of radioactive decay of any unstable nucleus, in terms of its half life. 

Gamma emission is the release of high-energy, short-wavelength photons, which are similar to x-rays. The representation of this radiation is y. Gamma emission commonly accompanies most other types of radioactive decay, but we normally do not show it in the balanced nuclear equation since it has neither appreciable mass nor charge. 

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

If we apply these equations to the condensation of a fission product in a cooling nuclear fireball, we must deal with sources from radioactive growth, sinks from radioactive decay, and dynamic conditions of temperature drop. In the simple case of radioactive 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... 

Consider the nuclei 15C, 15N, and 150. Which of these nuclei is stable What types of radioactive decay would the other two undergo Calculate the binding energy difference between 15N and 150. Assuming this difference comes from the Coulomb term in the semiempirical binding energy equation, calculate the nuclear radius. 

When a radionuclide decays, it does not disappear but is transformed into a new nuclear species of higher binding energy and often differing Z, A, J, tt, and so on. The equations of radioactive decay discussed so far have focused on the decrease of the parent radionuclides but have ignored the formation (and possible decay) of daughter, granddaughter, and so forth, species. It is the formation and decay of these children that is the focus of this section. 

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. 

The nuclear equation of this radioactive decay can be written... 

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 ... 

Note that the daughter nucleus has two fewer protons and two fewer neutrons than the parent, resulting in a different element. In this particular case, uranium has decayed to thorium. In radioactive decay equations, the total mass number A on the left side must equal the total mass number on the right. In the example above, Afefttotal = 235, while Anghttotal = 231 + 4 = 235. In addition, the total proton number on the left side of the equation must be equal to total proton number on right side (92 = 90 4- 2). So, in any nuclear reaction, there is conservation of mass number and charge. 

The fifth type of radioactive emission, gamma radiation, does not result in a change in the properties of the atoms. As a result, they are usually omitted from nuclear equations. Gamma emissions often accompany other alpha or beta reactions—any decay that has an excess of energy that is released. For example, when a positron collides with an electron, two gamma rays are emitted, a phenomenon usually referred to as annihilation radiation. 

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) ... 

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. 

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

Apply your knowledge of radioactive decay to write balanced nuclear equations. 

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. 

In the first steps of its radioactive decay series, thorium-232 decays to radium-228, which then decays to actinium-228. What are the balanced nuclear equations describing these first two decay steps ... 

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