The Bohr Model of the Atom

  December 20, 2021   Read time 4 min
The Bohr Model of the Atom
Rutherford’s nuclear model of the atom, while revolutionary, also caused a major scientific dilemma. Under the well-demonstrated laws of classical electromagnetic theory, a charge (like the orbiting electron) moving in a circular (or curved) path in an electrostatic field should lose energy.

Rutherford’s atomic nucleus model did not suggest any mechanism that would prevent an orbiting electron from losing its energy and falling into the positively charged nucleus under the influence of coulomb attraction. (Under the laws of electrostatics, like electric charges repel each other and unlike charges attract each other.) Because stable, electrically neutral atoms clearly existed in nature, scientists began to question whether classical electromagnetic theory was wrong. It took another revolution in thinking about the structure of the atom to resolve this dilemma.

In 1913, Bohr combined Max Planck’s quantum theory with Rutherford’s nuclear atom model and produced the Bohr model of the hydrogen atom. Bohr’s stroke of genius assumed that in the hydrogen atom, the electron could only occupy certain discrete energy levels or orbits as permitted by quantum mechanics. Scientists quickly embraced Bohr’s new atomic model because it provided a plausible quantum mechanical explanation for the puzzling line spectra of atomic hydrogen. As a result, Bohr’s pioneering work in atomic structure is considered the beginning of modern quantum mechanics.

Other talented physicists refined Bohr’s model and produced acceptable quantum mechanics models for atoms more complicated than hydrogen. These efforts included Werner Heisenberg’s uncertainty principle and Wolfgang Pauli’s exclusion principle. Using quantum mechanics, atomic scientists described the ground state electronic configurations of the elements in the periodic table in terms of configurations (or shells) of electrons in certain (allowed) energy states. The configuration of an atom’s outermost electrons determines its chemical properties.

As a result of Bohr’s intuition, a great quantity of elegant intellectual activity, both theoretical and experimental, took place in atomic physics. Bohr’s contemporaries extended his work and introduced a set of quantum numbers that describe the allowed patterns of electrons in multipleelectron atoms. This set includes the principal quantum number (n), which describes the energy level of the electron; the orbital quantum number (l), which describes the electron’s angular momentum (i.e., how fast a particular electron moves in its orbit around the nucleus); the magnetic quantum number (ml ), which describes the orientation of an electron in space; and, finally, the spin quantum number (ms ), which invokes the Pauli exclusion principle by requiring that two electrons can share the same orbit only if one spins clockwise and the other spins counterclockwise. Although a detailed discussion of this quantum model of atomic structure is beyond the scope of this book, a brief example follows to illustrate some of the marvelous intellectual achievement that took place in the two decades following the introduction of the Bohr atom.

Consider the ground state electronic configuration of the carbon atom. The quantum model of the atom assumes that all orbiting electrons with the same principal quantum number (n) are in the same shell. Therefore, the two electrons with n = 1 are in a single shell (traditionally called the K-shell). Similarly, electrons with n = 2 are in another shell (referred to as the L-shell). As the number of electrons increases, physicists assign additional shells to describe their orbits. For example, Figure 4.3 depicts the complex electron shell structure for the transuranic element californium (atomic number 98).

Atomic scientists find it convenient to treat orbiting electrons with the same values of the n and l quantum numbers as being in the same subshell. Therefore, the K-shell (for n = 1) consists of a single subshell, while the Lshell (corresponding to n = 2) has two subshells. For historic reasons, scientists refer to these subshells by a letter rather than the value of the appropriate orbital quantum number (l). Consequently, the l = 0 subshell is called the s subshell, while the l = 1 subshell is called the p subshell, and so forth, creating the traditional subshell designation sequence s (l = 0), p (l = 1), d (l = 2), f (l = 3), g (l = 4), h (l = 5), and so forth. The laws of quantum mechanics that describe the motions of the electrons around an atomic nucleus specify that the maximum number of electrons in any s subshell is 2, in any p subshell is 6, in any d subshell is 10, and in any f subshell is 14. For the neutral carbon atom, the ground state electronic configuration is conveniently described by the following quantum mechanics shorthand: 1s2 2s2 2p2. However, as shown in Figure 4.3, a description of the ground state configuration of the 98 electrons orbiting the nucleus of a californium atom is considerably more complex, with the 5f subshell determining the characteristic features of this transuranic element within the actinide series of elements.