Thus, if a certain amount of external energy is required to excite an electron from one energy level to another, that same amount of energy will be liberated when the electron returns to its initial state ( Figure 6.15). The law of conservation of energy says that we can neither create nor destroy energy. We can relate the energy of electrons in atoms to what we learned previously about energy. Similarly, if a photon is absorbed by an atom, the energy of the photon moves an electron from a lower energy orbit up to a more excited one. When an electron transitions from an excited state (higher energy orbit) to a less excited state, or ground state, the difference in energy is emitted as a photon. If the atom receives energy from an outside source, it is possible for the electron to move to an orbit with a higher n value and the atom is now in an excited electronic state (or simply an excited state) with a higher energy. When the electron is in this lowest energy orbit, the atom is said to be in its ground electronic state (or simply ground state). Thus, the electron in a hydrogen atom usually moves in the n = 1 orbit, the orbit in which it has the lowest energy. One of the fundamental laws of physics is that matter is most stable with the lowest possible energy. The lowest few energy levels are shown in Figure 6.14. Since the Rydberg constant was one of the most precisely measured constants at that time, this level of agreement was astonishing and meant that Bohr’s model was taken seriously, despite the many assumptions that Bohr needed to derive it.

When Bohr calculated his theoretical value for the Rydberg constant, R ∞, R ∞, and compared it with the experimentally accepted value, he got excellent agreement. Which is identical to the Rydberg equation in which R ∞ = k h c. The energy absorbed or emitted would reflect differences in the orbital energies according to this equation:ġ λ = k h c ( 1 n 1 2 − 1 n 2 2 ) 1 λ = k h c ( 1 n 1 2 − 1 n 2 2 ) Bohr assumed that the electron orbiting the nucleus would not normally emit any radiation (the stationary state hypothesis), but it would emit or absorb a photon if it moved to a different orbit. Instead, he incorporated into the classical mechanics description of the atom Planck’s ideas of quantization and Einstein’s finding that light consists of photons whose energy is proportional to their frequency. In 1913, Niels Bohr attempted to resolve the atomic paradox by ignoring classical electromagnetism’s prediction that the orbiting electron in hydrogen would continuously emit light.

This loss in orbital energy should result in the electron’s orbit getting continually smaller until it spirals into the nucleus, implying that atoms are inherently unstable. This classical mechanics description of the atom is incomplete, however, since an electron moving in an elliptical orbit would be accelerating (by changing direction) and, according to classical electromagnetism, it should continuously emit electromagnetic radiation. The electrostatic force attracting the electron to the proton depends only on the distance between the two particles. The simplest atom is hydrogen, consisting of a single proton as the nucleus about which a single electron moves. This picture was called the planetary model, since it pictured the atom as a miniature “solar system” with the electrons orbiting the nucleus like planets orbiting the sun.

Use the Rydberg equation to calculate energies of light emitted or absorbed by hydrogen atomsįollowing the work of Ernest Rutherford and his colleagues in the early twentieth century, the picture of atoms consisting of tiny dense nuclei surrounded by lighter and even tinier electrons continually moving about the nucleus was well established.

Describe the Bohr model of the hydrogen atom.

By the end of this section, you will be able to:

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