 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum  # Unit 3: Atoms and Light—Exploring Atomic and Electronic Structure

## Section 9: The Quantum Model

A Danish physicist, Niels Bohr (1885–1962) came up with the first model for the atom that explained the spectroscopic data that had been collected for the hydrogen atom. This was also the first model that used this idea of quantization, that energies come in these discrete packets of specific sizes. A former student of Ernest Rutherford, he applied the quantum approach to come up with a new structure of the atom. In 1913, Bohr postulated that the electrons orbit the nucleus at specific distances from the nucleus, and each orbit had a different energy associated with it. Each one of these energy levels corresponded to one of Rydberg's integers, with the lowest, n = 1, corresponding to the ground state, or lowest energy level.

When an atom absorbs energy, the electron jumps to a higher energy level. Then, it releases the energy in the form of a photon when it spontaneously falls back down to a lower energy level. One of Bohr's key insights was that an atom cannot absorb or give off energy at just any level. Instead, the energy is absorbed or emitted in discrete amounts, or quanta, as predicted by Max Planck. Bohr proposed that the lines in the emission spectrum of hydrogen correspond to specific changes in the energy of its sole electron. With only one electron, the hydrogen atom's electron had a very limited number of energy levels to jump between, and only four of those energies fell in the visible spectrum, which were those four colored lines in the Balmer series. Because these atoms can absorb light and jump up to higher levels or they can get excited to higher levels and fall back down and emit light, both emission and absorption spectra can be explained for hydrogen with the Bohr model of the atom. Figure 3-17. Energy Levels of a Hydrogen Atom

View More ### Figure 3-17. Energy Levels of a Hydrogen Atom

Bohr proposed that the different emission lines correspond to the transition of an electron from one energy level to another. In this schematic picture of the hydrogen atom, the different energy levels are labeled on the right. The transition from n = 3 to n = 2, a relatively small difference, gives rise to a particular red light (red arrow). The transition from n = 2 to n = 1, is a longer difference, therefore the photon given off has a higher energy (blue-green arrow). The biggest transition is from n = 3 to n = 1; this photon might be in the ultraviolet (purple arrow).

While Bohr's theory was a crucial step toward the development of quantum mechanics, unfortunately it worked very well for hydrogen with its one electron, but it didn't extend well to elements that had more than one electron.

Nonetheless, his theory held until 1926, when Austrian physicist Erwin Schrödinger (1887–1961) put forward a new mathematical framework to describe the energy levels of the hydrogen electron, the Schrödinger equation. The Schrödinger equation takes the mathematics that models waves, such as a ripple on a pond or the sound of a vibrating string, and applies them to describe the wavefunction of a particle, like the electron in an atom. This means that electrons behave as both particles and waves, according to quantum mechanics. This concept of the wave-particle duality states that all forms of electromagnetic energy, as well as atoms and subatomic particles, have both characteristics simultaneously: those of a wave and those of a particle. It was Louis de Broglie (1892–1987), a French prince and mathematician, who found a mathematical relationship between moving particles and their wavelike properties.

The quantum model of the atom is very complex; the equations of the wavefunctions are very complicated, but we can summarize the important things that come out of this final model of the atom. Rather than modeling the electron as a planet orbiting around a nucleus (or sun), these wavefunctions actually show regions of space where the electron is likely to be found. We still call these regions of space "orbitals," but it means we do not actually know where the electron is, just where we are likely to find it. These orbitals also come in a variety of shapes and sizes, and that information can also be pulled out of the Schrödinger equation and its wavefunction solutions. This means that at any point in time, the nucleus is surrounded by what we call a "cloud of electrons." In the next unit, we will talk more about these orbitals and the implications they have for the electrons held within them.

Taken together, all these discoveries, and more, form the basis of the quantum model of the atom, which is the current framework by which we understand the interactions of atoms and their electrons. This model can be used to explain the properties of the elements and how they combine to make chemical compounds simply by understanding how their electrons behave. These topics will be revisited in Unit 4 and other units in the course. However, we can summarize the model as follows:

• Atoms are composed of two separate parts: a small, dense, positively charged nucleus and a much larger, diffuse, and negatively charged cloud of electrons.
• Electrons in an atom must be in specifically allowed energy levels, which are called "orbitals." These are not specific places, but a region of space around the nucleus where the electron is likely to be found.
• As an atom absorbs or emits energy, an electron must move from one energy level to another. Most times, the form of energy involved in electronic transitions is light. Only certain specific energies of light can be absorbed or emitted by an atom of a specific element.

## Glossary

### Quantum model of the atom

A model of the atom that describes the electrons in the atom as having only very specific values of energy and locations in space.

### Schrödinger equation

A differential equation that, when solved for an atom, gives many possible solutions, corresponding to different possible wave functions for that atom. This equation is important in quantum mechanics because it demonstrates that an atomic orbital can be described as a probability distribution map of the position of an electron (rather than a rigidly defined orbital, in which the location of an electron can be known).

### Wave particle duality

In quantum mechanics, when fast moving particles of matter or photons of energy blur the lines between the wave-like nature of light and the particle-like nature of an object.

### Wavefunction

In the solutions to the Schrödinger equation, electrons can be associated with mathematical functions, called "wavefunctions," that relate to their energy and probable locations in space.