Atomic Structure Study Guide (page 2)
Electrons not only orbit around the nucleus of an atom, but they also move to higher and lower orbits also called higher and lower energy levels. These transitions require energy to move to a higher orbit and release energy to move to a lower orbit. The position of an electron can be identified by its unique set of four quantum numbers.
The electromagnetic spectrum represents all types of radiant energy (see Figure 9.1). All radiant energy travels at the speed of light (c = 2.998 * 108 m/s). Because this speed is constant and it is assumed that electromagnet radiation travels as a wave, the product of the wavelength λ (the distance between two equal points on a wave) times the frequency ν (the number of waves that pass a certain point in time) equals the speed of light or c = λν, where c = speed of light (2.998 * 108). Frequency units are in 1/s or Hertz (Hz).
Thomas Young described this radiation as a wave, but German physicist Max Planck described this radiation as a "quanta" of energy. Planck discovered that atoms release energy in specific quantities, which he called quanta. Albert Einstein was the first to recognize that electromagnetic radiation or light is a combination of quanta theory and wave theory. He suggested that a stream of particles called photons travels as a wave through space. Using Planck's theory and constant (h = 6.626 * 10–34 J s), he developed the energy of light or a photon:
Ephoton = hν or simply E = hν
Combining these equations gives
Calculate the energy of the photon if the wavelength is 3.62 * 106 nm.
- Convert nm to m (nanometers must be converted to meters because the speed of light is in meters):
3.62 * 106 nm * = 3.62 * 10–3m
- Calculate E:
5.49 * 10–23 J
Energy of the Hydrogen Electron
The neutral hydrogen atom has one electron in its ground state or ground level. The ground state is the lowest energy of the atom. The energy levels of anatom are designated by the letter n. Atoms have energy levels beginning with n =1 and when the electron is infinitely away from the nucleus at n = ∞ (see Figure 9.3).
When the electron "jumps" to a higher energy level, the electron is in an excited state or excited level. The electron in the excited state returns to the ground state and releases energy equal to the difference in the energy levels. An emission spectrum of an atom occurs when electrons move to lower energy levels. The chemistry of fireworks is based on the electron movement between the ground state and the excited states. Magnesium has a strong white emission spectrum and lithium has a strong red spectrum. The hydrogen atom energies can be calculated by using the following equation:
E = 2.18 * 10–18 J
The ni is the initial energy level and the nf is the final energy level of the electron. A decrease in the energy level (higher E to lower E) releases energy (minus value) and shows the emission process. However, an increase in the energy level shows the energy required (positive E) to excite the electron.
What is the energy release when the hydrogen electron goes from n = 5 to n = 2?
E = 2.18 * 10–18 J = 2.18 * 10–18 J
= – 4.58 * 10–19 J
What is the wavelength of the light needed to remove the hydrogen electron from its ground state?
- ni = 1 and nf = ∞ (completely removed from the atom)
- Calculate E:
E = 2.18 * 10–18 J = 2.18 * 10–18 J
= 2.18 * 10–18 J
- Calculate the wavelength:
9.11 * 10–8 m = 91.1 nm
Four quantum numbers describe the position and behavior of an electron in an atom: the principal quantum number, the angular momentum quantum number, the magnetic quantum number, and the electron spin quantum number. A branch of physics called quantum mechanics mathematically derives these numbers through the Schrödinger equation.
Principal quantum number ( n) The principle quantum number is the energy level of the electron given the designation n. The value of n can be any integer (1, 2, 3, 4 . . .) and determines the energy of the orbitals.
Angular momentum quantum number ( l) The angular momentum is the subshell designation of an electron and describes the shape of the orbital. These subshells are described by the letter l. The possible l values for a particular energy level are 0 to (n – 1). The l values are also given a letter designation. The l value is 0, 1, 2, 3, or 4, and the designation is s, p, d, f, or g.
Magnetic quantum number (ml) The magnetic quantum number (ml) describes the orbital's orientation in space. For a given l value, ml has integer values from –l to +l. In other words, for the p subshell (l = 1), the ml values are –1, 0, and +1, hence three orbitals.
Electron spin quantum number (ms) The electron spin quantum number describes the spin of an electron. Magnetic fields have shown that the two electrons in an orbital have equal and opposite spins. The ms values for these spins are and .
Are the following possible sets of quantum numbers? Explain.
(1, 1, 1, ); (2, 1, 0, ); (3, 2, 1, 1)
(1, 1, 1,): Not possible. For n = 1, l can only be 0, not 1.
(2, 1, 0, ): Possible.
(3, 2, 1, 1): Not possible. ms can only be or .
Practice problems for these concepts can be found at - Atomic Structure Practice Questions
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