FHSST Physics/Atom/Successive Ionization Energies

Successive ionization energies to provide evidence for arrangement of electrons into core and valence

[Brink and Jones sections: de Broglie - matter shows particle and wave characteristics, proved by Davisson and Germer. Shroedinger and Heisenberg developed this model into quantum mechanics]

The nucleus (atomic nucleus) is the center of an atom. It is composed of one or more protons and usually some neutrons as well. The number of protons in an atom's nucleus is called the atomic number, and determines which element the atom is (for example hydrogen, carbon, oxygen, etc.).

Though the positively charged protons exert a repulsive electromagnetic force on each other, the distances between nuclear particles are small enough that the strong interaction (which is stronger than the electromagnetic force but decreases more rapidly with distance) predominates. (The gravitational attraction is negligible, being a factor 1036 weaker than this electromagnetic repulsion.)

The discovery of the electron was the first indication that the atom had internal structure. This structure was initially imagined according to the "raisin cookie" or "plum pudding" model, in which the small, negatively charged electrons were embedded in a large sphere containing all the positive charge. Ernest Rutherford and Marsden, however, discovered in 1911 that alpha particles from a radium source were sometimes scattered backwards from a gold foil, indicating that there must be a dense concentration of positive charge at the center of the atom. This discovery led to the acceptance of a planetary model, in which the electrons orbited a tiny nucleus in the same way that the planets orbit the sun.

Interesting Fact: The word atom is derived from the Greek atomos, indivisible, from a-, not, and tomos, a cut.

An atom is the smallest portion into which a chemical element can be divided while still retaining its properties. Atoms are the basic constituents of molecules and ordinary matter. Atoms are composed of subatomic particles.

Atoms are composed mostly of empty space, but also of smaller subatomic particles. At the center of the atom is a tiny positive nucleus composed of nucleons (protons and neutrons). The rest of the atom contains only the fairly flexible electron shells. Usually atoms are electrically neutral with as many electrons as protons.

Atoms are generally classified by their atomic number, which corresponds to the number of protons in the atom. For example, carbon atoms are those atoms containing 6 protons. All atoms with the same atomic number share a wide variety of physical properties and exhibit the same chemical behavior. The various kinds of atoms are listed in the Periodic table. Atoms having the same atomic number, but different atomic masses (due to their different numbers of neutrons), are called isotopes.

The simplest atom is the hydrogen atom, having atomic number 1 and consisting of one proton and one electron. It has been the subject of much interest in science, particularly in the early development of quantum theory.

The chemical behavior of atoms is largely due to interactions between the electrons. In particular the electrons in the outermost shell, called the valence electrons, have the greatest influence on chemical behavior. Core electrons (those not in the outer shell) play a role, but it is usually in terms of a secondary effect due to screening of the positive charge in the atomic nucleus.

There is a strong tendency for atoms to completely fill (or empty) the outer electron shell, which in hydrogen and helium has space for two electrons, and in all other atoms has space for eight. This is achieved either by sharing electrons with neighboring atoms or by completely removing electrons from other atoms. When electrons are shared a covalent bond is formed between the two atoms. Covalent bonds are the strongest type of atomic bond.

When one or more electrons are completely removed from one atom by another, ions are formed. Ions are atoms that possess a net charge due to an imbalance in the number of protons and electrons. The ion that stole the electron(s) is called an anion and is negatively charged. The atom that lost the electron(s) is called a cation and is positively charged. Cations and anions are attracted to each other due to coulombic forces between the positive and negative charges. This attraction is called ionic bonding and is weaker than covalent bonding.

As mentioned above covalent bonding implies a state in which electrons are shared equally between atoms, while ionic bonding implies that the electrons are completely confined to the anion. Except for a limited number of extreme cases, neither of these pictures is completely accurate. In most cases of covalent bonding, the electron is unequally shared, spending more time around the more electronegative atom, resulting in the covalent bond having some ionic character. Similarly, in ionic bonding the electrons often spend a small fraction of time around the more electropositive atom, resulting in some covalent character for the ionic bond.

Models of the atom

• Democritus' shaped-atom model (for want of a better name)
• The plum pudding model
• Cubical atom
• The Bohr model
• The quantum mechanical model

The Plum pudding model of the atom was made after the discovery of the electron but before the discovery of the proton or neutron. In it, the atom is envisioned as electrons surrounded by a soup of positive charge, like plums surrounded by pudding. This model was disproved by an experiment by Ernest Rutherford when he discovered the nucleus of the atom.

The Bohr Model is a physical model that depicts the atom as a small positively charged nucleus with electrons in orbit at different levels, similar in structure to the solar system. Because of its simplicity, the Bohr model is still commonly used and taught today.

In the early part of the 20th century, experiments by Ernest Rutherford and others had established that atoms consisted of a small dense positively charged nucleus surrounded by orbiting negatively charged electrons. However, theoretical predictions and experimental evidence quickly began to cast doubt on the classical orbital model.

The simplest possible atom is hydrogen, which consists of a positively charged proton and a negatively charged orbiting electron. According to the orbital model of the atom, since the nucleus (the proton) and the electron are oppositely charged they will attract one another by coulomb force, in the same way that the Sun attracts the Earth with the gravitational force. However, if the electron orbits the nucleus in a classical orbit, it is undergoing a central acceleration, and ought to emit electromagnetic radiation (light) according to well established theories of electromagnetism. If the orbiting electron radiates as it orbits, it must lose energy and therefore spiral into the nucleus in a very short time, which clearly does not occur.

Also, it was well known at the time that atoms emit light only at certain frequencies - the frequencies at which an atom can radiate are known as the spectra of the atom. It was clear that the emission of light by atoms was due to electrons radiating. However, if the electrons are simply orbiting the nucleus classically like planets, there is no reason for the spectra - one would expect the electrons to emit radiation in a continuous frequency spectrum. It soon became clear that something was very wrong with the orbital description of the atom.

These difficulties were resolved in 1913 by Niels Bohr who proposed that:

• (1) The orbiting electrons existed in orbits that had discrete quantized energies. That is, not every orbit is possible but only certain specific ones. The exact energies of the allowed orbits depends on the atom in question.
• (2) The laws of classical mechanics do not apply when electrons make the jump from one allowed orbit to another.
• (3) When an electron makes a jump from one orbit to another the energy difference is carried off (or supplied) by a single quantum of light (called a photon) which has a frequency that directly depends on the energy difference between the two orbitals.

$f=E/h$

where f is the frequency of the photon, E the energy difference, and h is a constant of proportionality known as Planck's constant. Defining we can write

where ?? is the angular frequency of the photon.

• (4) The allowed orbits depend on quantized (discrete) values of orbital angular momentum, L according to the equation

Where n = 1,2,3, and is called the angular momentum quantum number.

These assumptions explained many of the observations seen at the time, such as why spectra consist of discrete lines. Assumption 4) states that the lowest value of n is 1. This corresponds to a smallest possible radius (for the mathematics see Ohanian-principles of physics or any of the large, usually American, college introductory physics textbooks) of 0.0529 nm. This is known as the Bohr radius, and explains why atoms are stable. Once an electron is in the lowest orbit, it can go no further. It cannot emit any more light because it would need to go into a lower orbit, but it can't do that if it is already in the lowest allowed orbit.

The Bohr model is sometimes known as the semiclassical model because although it does include some ideas of quantum mechanics it is not a full quantum mechanical description of the atom. Assumption 2) states that the laws of classical mechanics don't apply during a quantum jump but doesn't state what laws should replace classical mechanics. Assumption 4) states that angular momentum is quantised but does not explain why.

In order to fully describe an atom we need to use the full theory of quantum mechanics, which was worked out by a number of people in the years following the Bohr model. This theory treats the electrons as waves, which create 3D standing wave patterns in the atom. (This is why quantum mechanics is sometimes called wave mechanics.) This theory considers that idea of electrons as being little billiard ball like particles that travel round in orbits as absurdly wrong instead electrons form probability clouds. You might find the electron here with a certain probability; you might find it over there with a different probability. However it is interesting to note that if you work out the average radius of an electron in the lowest possible energy state it turns out to be exactly equal to the Bohr radius (although it takes many more pages of mathematics to work it out).

The full quantum mechanics theory is a beautiful theory that has been experimentally tested and found to be incredibly accurate, however it is mathematically much more advanced, and often using the much simpler Bohr model will get you the results with much less hassle. The thing to remember is that it is only a model, an aid to understanding. Atoms are not really little solar systems.

• See also: Hydrogen atom, quantum mechanics, Schr&ouml dinger equation, Niels Bohr.
• An interactive demonstration http://webphysics.davidson.edu/faculty/dmb/hydrogen/ of the probability clouds of electron in Hydrogen atom according to the full QM solution.