Electron Shells

Stable isotopes of helium

Î2 protons \l neutron

2 electrons

Î2 protons \l neutron

2 electrons

electrons protons neutrons electrons protons neutrons

Fig. F.1. The stable isotopes of helium that contain two electrons. Helium-3, 32He contains 2 protons and one neutron, while the much more abundant helium-4, 42He, contains 2 protons and 2 neutrons.

Not only can atoms gain and lose electrons, they can share them in covalent bonds. When they do, all the shared electrons contribute to filling vacancies in the outer electron shell of each atom. The helium atom with filled shell, Figure F.1, is stable and does not form molecules.

The innermost shell (called the 1s or K shell) in any atom can hold a maximum of only two electrons, and the second shell (denoted by L shell) can hold eight. A helium atom has its single shell filled with two electrons.

F-2.1 The Bohr Atom: In 1913 Niels Bohr proposed a model for the hydrogen atom in which the electron moved in a circular orbit around the nucleus. Not all orbits were possible, according to Bohr, but only those that met certain conditions. The orbit with the smallest size would have one complete electron wave around its circumference; the next allowable orbit would have two complete waves, and then three, four, and so on. The only allowed orbits were those for which the total circumference was an integral number n of wavelengths. The orbits are shown in Figure F.2. The radius a0 of the smallest orbit is known as the Bohr radius, with a value of 0.53 X 10~8 cm, where 10~8 cm = 1 angstrom (A).

The energy corresponding to the orbital state n of the hydrogen atom is given by where E0 is another collection of physical constants, which for hydrogen has a value of 13.6 eV. The allowed energy levels for hydrogen are diagramed in Figure F.3. By convention, energy is expressed relative to that of an ionized atom, with the electron at rest but infinitely far away. The energy of any atom with its electron still bound to it must be less

Fig. F.2. Radii of orbits in the Bohr model of the hydrogen atom where a0 is the Bohr radius and n is an integer.

than zero or negative. Positive energy refers to the kinetic energy of the removed electron if it is not at rest. For atomic hydrogen, the lowest-energy state, with the 0.53 radius orbit, has an energy of E1 = 13.6 eV.

Atomic hydrogen in this state is 13.6 eV more stable than an ionized atom. Thus 13.6 eV is the ionization energy of atomic hydrogen. Although the numerical value is calculated from first principles in the Bohr theory, it agrees exactly with the measured value of the ionization energy of hydrogen.

F-2.2 Wave Mechanics: A

quantum or wave theory was developed in the 1920s by Erwin Schrödinger and Werner Heisenberg. As in the simpler Bohr theory, the energy of an electron in an atom is restricted to certain values, or is quantized. Four quantum numbers instead of one are required to describe the state of an electron in an atom, and they are designated n, l, m, and Ms. The average distance of the electron

Fig. F.3. Energy levels of allowed orbits in the Bohr model of the hydrogen atom. The energy levels are depicted as constrained in a potential well established by the positive charge of the proton in the nucleus of the hydrogen atom. The energy levels En are given by E0/n2 with E0 = 13.58 eV, which represents the ionization energy required for complete removal of the n = 1 electron.

Fig. F.3. Energy levels of allowed orbits in the Bohr model of the hydrogen atom. The energy levels are depicted as constrained in a potential well established by the positive charge of the proton in the nucleus of the hydrogen atom. The energy levels En are given by E0/n2 with E0 = 13.58 eV, which represents the ionization energy required for complete removal of the n = 1 electron.

from the nucleus depends primarily on n, which is called the principal quantum number. The geometry of bonding around the atom depends primarily on quantum number 1, called the orbital-shape, or azimuthal, quantum number. The energy of an electron in an atom is a function of n and to a lesser degree of l; usually, all m states for given n and l values have the same energy. There is a fourth quantum Ms, which denotes the spin of the electron. Electrons can have two spin states (spin up or down).

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