Radioative Decay

Types of Radioactive Decay
The type of radioactive decay that occurs usually depends on whether the nucleus is above or below or to the right of the stability belt.There are five common types of radioactive decay.
1.Alpha Emission
2.Beta Emission
3.Positron Emission
4.Electron Capture
5.Gamma Emission
Half-life period
The time required for half of a radioactive substance to disintegrate is known as the half-life period, represented here by t1/2
Radioactive Isotopes and Isobars
A radioactive isotope is formed by the emission of one alpha and bita paricles, while an isobar is formed by the emission of one bita particle.
Binding Energy of the Nucleus
It has been observed that the actual mass of an isotope of an element, obtained experimentally using mass spectrograph, is invariably less than the calculated mass of the isotope. This mass difference is known as mass defect of the nucleus which is also expressed as the packing fraction of the nucleus.
Packing fraction = isotopic mass - mass number/mass number x 10000

Neutron-Proton Ratio and Nuclear Stability

Most naturally occurring nuclides hav even numbers of neutrons and even numbers of protons. Nuclides with odd numbers of both neutrons and protons are least common and those with odd-even combinations are intermediate in abundance.
No. of protons even even odd odd
No. of neutrons even even even odd
No. of stable nuclides 157 52 50 5
A plot of the number of neutrons versus the number of protons shws that as the atomic number increases, the N/P ratio of the stable nuclides increases.

Quantum Numbers and Electronic Configuration

The following rules help us to predict electronic configuration
of atoms with the help of quantum numbers
1. Electrons are added into orbitals in the way that gives the
lowest total energy for the atom.
2. Electrons are assigned to orbitals in order of increasing
value of (n+l).
3. For subshells with the same value of (n+l), electrons are
assigned first to the subshell with lower n.
4. No two electrons in an atom may have identical sets of four
quantum numbers.
5. Electrons occupy all the orbitals of a given subshell singly
before pairing begins. These unpaired electrons have parallel
spins. (Hund Rule). Hund rule states that for degenerate
orbitals, the lowest energy is attained when the number of
electrons with the same spin is maximized.

Atomic Stucture

An atom consists of extremely small and dense nucleus and an extra nuclear space. The nucleus contains positively charged protons and neutrons, and these particles are collectively called nucleons. In the extra nuclear space, negatively charged electrons revolve around the nucleus. As the magnitude of the charge of an electron is the same as that of a proton, the number of electrons is equal to that of protons in an atom, the atom being neutral.The number of protons present in the nucleus of an atom is termed as the atomic number of the element (Z). The sum of the number of protons and neutrons is called the mass number (A). The term 'nuclide' refers to a nucleus having a specific atomic number and specific mass number.To calculate the radius (r) and energy (E) of a permissible orbit for one electron species Bohr derived equations based on the following postulates.
Bohr's Postulates
1. The electrons revolve around the nucleus in certain orbits without losing energy because the energy in a fraction of a quantum can neither be lost nor gained.
2 Energy is absorbed or emitted only when an electron in an atom jumps from one orbit to another.
3 The electron is restricted to those orbits in which its angular momentum is an integral multiple of h/2pie Angular momentum = mvr= n x h/2pie
Failure of Bohr Theory
1 It does not explain the spectra of species having more than one electron.
2 It does not explain the fine spectral lines obtained under a spectroscope of strong resolution. However, it can be explained by Bohr-Sommerfeld theory of elliptical orbits.
3 It does not explain Zeeman effect, that is, splitting of spectral lines under magnetic field, and Stark effect, that is, splitting of spectral lines under electric field.

Empirical, Molecular and Structural Formalae

The utility of the mole concept is further illustrated by the
problems of determining the empirical and molecular formulae of
the compounds. Empirical formula represents the simplest set of
whole numbers expressing the relative numbers of atoms in the
compound and anything that can be said about relative numbers of
atoms may be said about the relative numbers of moles of atoms. A
calculation of the relative numbers of moles of each element in
the compound will, therefore, lead us to the empirical formula of
the compound. The empirical formula implies nothing about how
many moles of atoms are actually in one mole of the compound.In fact, the molecular formula expresses the actual numbers of moles of atoms of each element present in one mole of the compound. The molecular formula weight is the whole number multiple of the empirical formula weight for a given compound.Molecular formula weight/Empirical formula weight = n(say)Thus if X represents the empirical formula of a compound, its molecular formula will be represented as (X)n.

Electrolytic Concuctance

The passage of a current through an electrolyte involves the movement of ions carrying an electric charge and so the study of electrolytic conduction may supply useful chemical information.The magnitude of the conductance, i.e., the reciprocal of resistance, depends mainly on three factors: the number of ions, magnitude of charge on each ion and the ionic mobility.The conductance of an electrolyte may be measured in terms of molar conductance, that is, the conductance due to one mole of an ionic solute and secondly, the equivalent conductance, that is, the conducting power of all ions produced by one equivalent of the electrolyte in the given solution. But to compare the conductance of two solutions, equivalent conductance is considered because one equivalent of different electrolytes involves the same number of electrons in accordance with Faraday's second law of electrolysis while one mole of different electrolytes may or may not involve the same number of electrons. In other words, the solutions, each containing one equivalent of different electrolytes, are equivalent in terms of moles of electrons being carried.

Importance of Faraday's law

The electrical and chemical concepts are interdependent. A flow of electricity through a substance may produce a chemical reaction, and also, a chemical reaction may cause a flow of electricity through some external circuit. The former involves the study of electrolysis and conductance, while the latter, the measurement of electromotive force.
Electrolysis
Faraday's law The quantitative relationship between the amount of electricity passed through a cell and the amount of substances discharged at the electrodes was systematised by Michael Faraday in the form of the following laws:
First law : The amount of substance discharged at an electrode is proportional to the quantity of the electricity passing through the electrolyte.
Second law: When the same quantity of electricity is passed through different solutions, the amount of different substances deposited or dissolved at the electrodes in different electrolytic cells are proportional to their equivalent weights, and in an electrolytic cell, chemically equivalent amounts or substances are discharged at both the electrodes.
The essential content of Faraday's second law is that 1 Faraday, which corresponds to 1 mole of electrons, liberates 1 equivalent of matter. In redox reactions, the amount of the reactant, corresponding in 1 mole of electrons, is thus its equivalent mass.