Chemistry for Liberal Studies - Forensic Academy / Dr. Stephanie R. Dillon

# Electronic Structure & Light Now that you are familiar with the structure of the atom, we can further explore how the structure and the light generated from each element are related. In order to understand this relationship we need to look at the model of the atom proposed by Neils Bohr. Bohr stated that the structure of an atom had specific energy levels in which the electrons were located around the nucleus.

Whenever an electron moves from one of these energy levels to another it must either gain or lose some energy. If the electron gains energy this is called an absorbance and if it lost energy this is called an emittance. In both cases an energy particle called a PHOTON is absorbed or emitted and thus light is absorbed or emitted. Different elements have different energy levels so that is why different elements emit or absorb different amounts (wavelengths) of light.

Before going on we need to define a couple of terms often used to describe light: ### Wavelength

The wavelength ($\lambda$) of light is defined as the distance between the crests or troughs of a wave motion. Wavelengths found in the electromagnetic spectrum (range of light) can be measured in units as large as 103 meters (radio waves) to 10-11 meters (gamma waves). For the wavelengths of visible light (the light we see in color) the most common units used are nanometers (10-9 meters) and Angstroms (10-10 meters).

### Frequency

Frequency ($\nu$) is the number of occurrences of a repeating event per unit time. In the case of light, frequency refers to the number of times a wavelength is repeated per second. The unit used most often to describe frequency is Hz which means "per second" or /s.

The relationship between wavelength and frequency is related through the speed of light.

$$c = \lambda \nu$$

c is the speed of light, 3.00 x 108 m/s. If you know the frequency you can easily convert to wavelength using the speed of light and vice versa.

The full electromagnetic spectrum is generally shown with both measurements given: The wavelengths and frequencies of the light emitted by an atom (its emission spectrum) is determined by its electronic structure. In the Bohr model shown above you can see that as each electron moves from a higher energy level (orbit) to a lower one, a different color is emitted. The numbers shown above the colors are the wavelengths that correspond to the color. Each shade of color has a unique wavelength based on the unique distance and energy. The Bohr model consists of four principles:

1. Electrons assume only certain orbits around the nucleus. These orbits are stable and called "stationary" orbits.
2. Each orbit has an energy associated with it. For example the orbit closest to the nucleus has an energy E1, the next closest E2 and so on.
3. Light is emitted when an electron jumps from a higher orbit to a lower orbit and absorbed when it jumps from a lower to higher orbit.
4. The energy and frequency of light emitted or absorbed is given by the difference between the two orbit energies, e.g.

Bohr also assumed that the electron can change from one allowed orbit to another:

• Energy must be absorbed for an electron to move to a higher state (one with a higher n value)
• Energy is emitted when the electron moves to an orbit of lower energy (one with a lower n value)
• The overall change in energy associated with "orbit jumping" is the difference in energy levels between the ending (final) and initial orbits:

$$\Delta E(light) = E_f - E_i$$

When an electron "falls" from a higher orbit to a lower one the energy difference is a defined amount and results in emitted electromagnetic radiation of a defined energy ($\Delta E$)

Therefore, if the emitted radiation from a falling electron produces light and has a defined energy, then it must have a correspondingly defined frequency or wavelength:

$$\Delta E = R_H \ast \left(\frac{1}{n_i^2} - \frac{1}{n_f^2} \right) = h\nu$$

Gary, I would like to stop this animation when it gets to the page on "what does this have to do with the sun?" if possible.

Where RH is called the Rydberg constant and has a value of -2.18 x 10-18 J. This relationship was defined in part by another scientist, Max Planck. Planck had deduced that the energy of the photons comprising EM (electromagnetic) radiation is a function of its frequency (E = h$\nu$), this Planck's equation.

### Planck's Equation

In Planck's assumption, radiant energy is emitted in small bursts, known as "quanta". Each of the bursts called a "quantum" has energy E that depends on the frequency $\nu$ of the electromagnetic radiation by the equation:

$$E = h\nu$$

where $h$ is a fundamental constant of nature, the "Planck constant".

$$6.626 \times 10^{-34} J.s$$

This equation is later found to be true for all EM radiant energy emitted or absorbed.
**Planck's equation implies the higher the frequency of a radiation, the more energetic are its quanta.

So through Bohr's equation we can relate the energy to the structure of the atom, and through Planck's equation we can relate the frequency of light to the energy, and we already know how to relate the frequency to the wavelength and therefore the color of light. What we need to clarify at this point is how all of this information will help us understand the use of spectroscopy for investigation.