Mumbai University > Mechanical Engineering > Sem 7 > Power Plant Engineering

Marks : 10M

Year: Dec 2015

RADIOACTIVITY

Radioactivity is an important source of energy for small power devices and a source of radiation for use in research, industry, medicine, and a wide variety of applications, as well as an environmental concern. Most of the naturally occurring isotopes are stable. Those that are not stable, i.e., radioactive, are some isotopes of the heavy elements thallium (Z = 81), lead (Z = 82), and bismuth (Z = 83) and all the isotopes of the heavier elements beginning with polonium (Z = 84). A few lower-mass naturally occurring isotopes are radioactive, such as K40, Rb87 and In115. In addition, several thousand artificially produced isotopes of all masses are radioactive. Natural and artificial radioactive isotopes, also called radioisotopes, have similar disintegration rate mechanisms. Fig. 10.5 shows a Z-N chart of the known isotopes.

Radioactivity means that a radioactive isotope continuously undergoes spontaneous (i.e., without outside help) disintegration, usually with the emission of one or smaller particles from the parent nucleus, changing it into another, or daughter, nucleus. The parent nucleus is said to decay into the daughter nucleus. The daughter may or may not be stable, and several successive decays may occur until a stable isotope is formed.

An example of radioactivity is 49In115 = 50Sn115 + –1e0 Radioactivity is always accompanied by a decrease in mass and is thus always exothermic. The energyliberated shows up as kinetic energy of the emitted particles and as y radiation. The light particle is ejected at high speed, whereas the heavy one recoils at a muchslower pace in an opposite direction.Naturally occurring radio isotopes emit α, 3, or y particles or radiations. The artificial isotopes, in addition to the above, emit or undergo the following particles or reactions: positrons; orbital electron absorption, called K capture; and neutrons. In addition, neutrino emission accompanies βemission. αγ

Alpha decay: Alpha particles are helium nuclei, each consisting of two protons and two neutrons. They are commonly emitted by the heavier radioactive nuclei. An example is the decay of Pu239 into fissionable U235 94Pu239 = 92U235 + 2He4

Beta decay: An example of β decay is 82Pb214 = 83Bi214 + –1e0 + v Where v, is often dropped from the equation. The penetrating power of β particles is small compared with that of y-rays but is larger than that of particles. 6- and a-particle decay is usually accompanied by the emission of y radiation.

Gamma radiation: This is electromagnetic radiation of extremely short wavelength and very high frequency and therefore high energy. γ-rays and X-rays are physically similar but differ in their origin and energy: γ-rays from the nucleus, and X-rays from the atom because of orbital electrons changing orbits or energy levels. Gamma wave-lengths are, on an average, about one-tenth those of X-rays, although the energy ranges overlap somewhat. Gamma decay does not alter either the atomic or mass numbers.

In neutron decay the daughter is an isotope of the parent. Though it occurs rarely, it, however, comes about in nuclear reactors yielding delayed fission neutrons which greatly influence the reactor control. The rate of decay is a function only of the number of radioactive nuclei present at a time, provided that the number is large. It does not depend on temperature, pressure or the physical and chemical states of matter, i.e whether it is in solid, liquid or gaseous phase, or in chemical combination with other atoms. If N be number of radioactive nuclei of one species at any time θ, the rate of decay

$\frac{-dN}{dθ}$=λN ------------- (1)

Where λ is a constant of proportionality, called the decay constant, having different values for different isotopes, with the

dimension $s^(-1)$. By integrating the above, we obtain a simple exponential relation,

N=$N _0 e^(-λθ)$ ------------- (2)

Where $N_0$ = radioactive atoms present at time θ = 0 and N = radioactive atoms present at time θ

The rate of decay $\frac{-dN}{dθ}$ is also called activity, A, and has the dimension of disintegration per second or dis/s or $s^(-1)$.

Thus from eqs (1) and (2)

A= $\frac{-dN}{dθ}$=λN=$λN_0 e^(-λθ)=A_0 e^(-λθ)$ -------- (3)

The decay rate is often expressed in the form of half-life, θ_(1/2) i.e the time during which one-half of the number of \radioactive species decays. Thus,

$\frac{N}{N_0} =\frac{A}{A_0} =\frac{1}{2}=e^-λθ_(\frac{1}{2})$

Or

$θ_(1/2)=\frac{(In 2)}{λ}=\frac{0.6931}{λ}$ ----------- (4)

Thus, half-life is inveraely proportional to the decay constant. Stating with N_0 half of N_0 decay after one half-life; one-half of the remaining atoms or ¼ of N_0 decay during the second half-life and so on.

Half-lives of radioactive isotopes differ by a wide range, varying from fractions of a microsecond to billions of years. No. two radioisotopes