D2.3 Atomic Energy Levels

Why should a hydrogen atom emit only four specific colors of visible light? To understand this better, we need to know more about the energy of the atom and how energy depends on atomic structure. An atom consists of a tiny nucleus surrounded by one or more electrons. The simplest atom, a hydrogen atom, has one proton as the nucleus and one electron outside the nucleus. According to Coulomb’s law, the electron and proton attract.

Exercise: Electrostatic Potential Energy

Activity: Line Spectra and Energies

Think about the implications of line spectra. If a hydrogen atom emits only four specific wavelengths in the visible region, what does this imply regarding the energies of the emitted photons? Why should only these four wavelengths be emitted, but none of the other possible wavelengths? Write your explanation in your notebook.

The model currently used to describe the distribution of electrons in an atom has these attributes:

  • The energies of electrons in an atom are restricted to energy levels, which are specific allowed energies.
  • Each line in the spectrum of an element results when an electron’s energy changes from one energy level to another; a change from one electronic energy level to another is called an electronic transition.
  • Electrons are distributed in regions centered on the nucleus, called shells; each shell has a different average distance from the nucleus.
  • As described by Coulomb’s law, an electron’s energy increases with increasing average distance from the nucleus; that is, with increasing size of an electron shell.
  • Both energy levels and shells are described by quantum numbers, numbers restricted to specific allowed values; the electron energies are said to be quantized, restricted to discrete energy levels.

An atom is most stable when it has the lowest possible energy. The lowest energy electronic state of an atom is called its electronic ground state (or simply ground state). Any higher energy state of an atom is called an electronic excited state (or simply an excited state).

The figure below shows the first few energy levels of a hydrogen atom. The atom is in its ground state when its electron is in the n = 1 (lowest energy) level. When a photon is absorbed by a ground state hydrogen atom, as shown on the left side of the figure, the energy of the photon moves the electron to a higher n (higher energy) level, and the atom is now in an excited state.

An atom in an excited state can release the extra energy as a single photon if the electron returns to its ground state (say, from n = 5 to n = 1), or the energy can be released as two or more lower energy photons if the electron falls to an intermediate state then to the ground state (say, from n = 5 to n = 2, emitting one photon, then from n = 2 to n = 1, emitting a second photon).

he figure includes a diagram representing the relative energy levels determined by the quantum numbers of the hydrogen atom. An upward pointing arrow at the left of the diagram is labeled, “E.” Long, horizontal line segments are placed to the right of the arrow. Labels to the right of each line segment are arranged in columns with the headings, “n” and “Energy.” The bottom horizontal line segment is labeled, “1” and “-2.179 aj.” At a level approximately three-quarters of the distance to the top a horizontal line segment is labeled “2” and “-0.545 aJ.” At a level approximately seven-eighths the distance from the bottom a green horizontal line segment is labeled “3” and “-0.242 aJ.” Just a short distance above this segment a line segment is labeled “4” and “-0.136 aJ.” Just above this segment a horizontal line segment is labeled “5” and “-0.097 aJ.” Just a short distance above this segment a horizontal line segment is labeled “infinity” and “0.0 aJ.” Arrows are drawn to depict energies of photons absorbed, as shown by upward pointing arrows on the left, or released as shown by downward pointing arrows on the right side of the diagram between the horizontal line segments. The label, “Electron moves to higher energy as light is absorbed,” is placed beneath the upward pointing arrows. Similarly, the label, “Electron moves to lower energy as light is emitted,” appears beneath the downward pointing arrows. Moving left to right across the diagram, arrows extend from one horizontal line segment to the next in the following order: 1 to 2, 1 to 3, 1 to 4, 1 to 5, 1 to infinity, 2 to 3, 2 to 4, and 2 to 5. The arrows originating from the segment labeled 1 are grouped together by close placement of the arrows. Similarly, the downward arrows follow in this sequence; infinity to a, 5 to 1, 4 to 1, 3 to 1, 2 to 1, 5 to 2, 4 to 2, and 3 to 2. Arrows are again grouped by close placement according to the horizontal segment at which the arrows end. Three of the downward pointing arrows are colored. The one from 5 to 2 is violet; the one from 4 to 2 is cyan; the one from 3 to 2 is red. These colors correspond to the colors of the visible lines in the H atom spectrum at 434.1 nm, 486.2 nm, and 656.4 nm.
Figure: Hydrogen-atom Energy Levels. The horizontal lines show the relative energy levels in the modern model of the hydrogen atom, and the vertical arrows depict the energy of photons absorbed (left) or emitted (right) as electrons move between these levels. The n = 1-5 levels are shown explicitly; the energy levels are closer together as n→∞. As n→∞, potential energy approaches zero. (Colored arrows show the colors of visible emissions.)
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Chemistry 109 Fall 2021 Copyright © by John Moore; Jia Zhou; and Etienne Garand is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.