Physics

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Electronic structures

We have mentioned that the electrons don't just orbit the nucleus in a haphazard way. They occupy energy levels or shells at different distances from the centre of the atom. Electrons always occupy the lowest available energy level.

The lowest energy level (the one found nearest to the nucleus) can hold just two electrons. Some people refer to this as the first or innermost shell.

The second energy level can hold eight electrons, as can the third energy level (although this can hold an extra ten in reserve, but you don't need to learn about that unless you study chemistry at a higher level).

This arrangement is summarized in this table:

Energy level Number of electrons it holds

1st 2

2nd 8

3rd 8

The energy levels fill up with electrons from the lowest energy level (innermost shell) and build up outwards. They only start occupying a new energy level when the previous one has been filled.

name symbol orbital meaning range of values value example

principal quantum number

shell

Chlorine can be found on many different locations all over the world. Chlorine is always found in compounds, because it is a very reactive element. Chlorine can usually be found bond to sodium (Na), or in kitchen salt (sodium chloride; NaCl). Most chlorine can be found dissolved in seas and salty lakes. Large quantities of chlorine can be found in the ground as rock salts or halite. Chlorine (Cl2) is one of the most reactive elements; it easily binds to other elements. In the outer shell there is space left for another electron. This causes free, charged atoms, called ions, to form. It can also cause an extra eletron to form (a covalent bond; a chlorine bond), causing the outer shell to complete. Chlorine can form very stable substances, such as kitchen salt (NaCl). Sodium chloride, also known as common salt, table salt, or halite, is a chemical compound with the formula NaCl. Ionic Bonding

Sodium metal reacts with chlorine gas in a violently exothermic reaction to produce NaCl (composed of Na+ and Cl- ions):

2Na(s) + Cl2(g) -> 2NaCl(s)

These ions are arranged in solid NaCl in a regular three-dimensional arrangement (or lattice. The chlorine has a high affinity for electrons, and the sodium has a low ionization potential. Thus the chlorine gains an electron from the sodium atom. This can be represented using electron-dot symbols (here we will consider one chlorine atom, rather than Cl2). The arrow indicates the transfer of the electron from sodium to chlorine to form the Na+ metal ion and the Cl- chloride ion. Each ion now has an octet of electrons in its valence shell. Energetics of Ionic Bond Formation

The formation of ionic compounds (like the addition of sodium metal and chlorine gas to form NaCl) are usually extremely exothermic.

The loss of an electron from an element and the gain of an electron by a nonmetal.

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Electron energy levels in hydrogen

The Bohr model is accurate only for one-electron systems such as the hydrogen atom or singly-ionized helium. This section uses the Bohr model to derive the energy levels of hydrogen.

The derivation starts with three simple assumptions:

1) All particles are wavelike, and an electron's wavelength л, is related to its velocity v by:

where h is Planck's Constant, and me is the mass of the electron. Bohr did not make this assumption (known as the de Broglie hypothesis) in his original derivation, because it hadn't been proposed at the time. However it allows the following intuitive statement.

2) The circumference of the electron's orbit must be an integer multiple of its wavelength:

where r is the radius of the electron's orbit, and n is a positive integer.

3) The electron is held in orbit by the coulomb force. That is, the coulomb force is equal to the centripetal force:

where k = 1 / (4ре0), and qe is the charge of the electron.

These are three equations with three unknowns: л, r, v. After solving this system of equations to find an equation for just v, it is placed into the equation for the total energy of the electron:

Because of the virial theorem, the total energy simplifies to

Substituting, one obtains the energy of the different levels of hydrogen:

Or, after plugging in values for the constants,

Thus, the lowest energy level of hydrogen (n = 1) is about -13.6 eV. The next energy level (n = 2) is -3.4 eV. The third (n = 3) is -1.51 eV, and so on. Note that these energies are less than zero, meaning that the electron is in a bound state with the proton. Positive energy states correspond to the ionized atom where the electron is no longer bound, but is in a scattering state.

Rydberg Formula

The Rydberg formula describes the transitions or quantum jumps between one energy level and another. When the electron moves from one energy level to another, a photon is given off. Using the derived formula for the different 'energy' levels of hydrogen one may determine the 'wavelengths' of light that a hydrogen atom can give off.

The energy of photons that a hydrogen atom can give off are given by the difference of two hydrogen energy levels:

where nf means the final energy level, and ni means