**Comparing the Classical Shell Model to the Quantum Mechanical Model of the Atom**

The classical shell model of the atom is convenient to picture and explains many aspects (such as electron energy levels) of the atom well. However, in 1924, Louis de Broglie theorized that all matter had wave properties. This was later confirmed by electron beam diffraction experiements and elaborated on by Erwin Schrodinger in the development of quantum mechanics. The quantum mechanical model does not describe the electron as orbiting around a central nucleus; instead it describes the electron’s matter wave as a probable location of finding the electron within the atom. The region in space where the electron is likely to be found is called an orbital; the shapes of \(s\), \(p\), and \(d\) orbitals are shown below.

The shell model works well for the hydrogen atom and other one electron species. However, with multielectron species, it failed to predict atomic spectra in the way it did for the hydrogen atom. Werner Heisenberg's Uncertainty Principle stated that the position and speed of an object on the quantum scale could not be known simultaneously. Essentially, this put a limit on how distinctly information could be known on the quantum level and ushered in a new method of thinking about atoms in terms of quantum properties.

**Example 1. **

Which orbital has a spherical shape?

A. s

B. p

C. d

*Solution*

A. \(s\)

The \(s\) orbital is spherically symmetric.

**Example 2. **

Which phenomenon could not be explained by the classical shell model?

A. The periodic trend in atomic size.

B. The periodic trend in first ionization energy.

C. The atomic spectra of multielectron atoms.

*Solution*

C. The classical shell model could not explain the atomic spectra of multielectron atoms.

The classical shell model is able to explain the periodic trends of atomic size and first ionization energy.

**Example 3. **

The de Broglie wavelength of an object can be calculated using the formula \(\lambda = \frac{h}{m \cdot u}\) where \(h = \text{Planck's constant} = 6.626 \times 10 ^{-34} \text{ J}\cdot\text{s}\), \(m = \text{mass of object, in kg}\), and \(u = \text{speed of object, in}\frac{\text{ m}}{\text{ s}}\). What is the de Broglie wavelength of an electron (\(\text{mass} = 9.1\times 10 ^{-31}\text{ kg}\)) travelling at a speed of \(1.0\times 10 ^{6}\frac{\text{ m}}{\text{ s}}\)?

A. \(1.4\times 10 ^{10}\text{ m}\)

B. \(7.3\times 10 ^{-10}\text{ m}\)

C. \(3.8\times 10 ^{-5}\text{ m}\)

*Solution*

B. \(7.3\times 10 ^{-10}\text{ m}\)

For very small objects (such as the electron) travelling at high speeds, the wavelength is of a similar magnitude and is therefore important for describing the properties of the moving object. For macroscopic (large) objects, such as a travelling baseball, the wavelength associated with the motion is tiny compared to the size of the object.