Chapter 6: Electronic Structure of Atoms – Study Notes

Chapter 6: Electronic Structure of Atoms

6.1 The Wave Nature of Light

The study of the electronic structure of atoms begins with understanding the nature of light, which exhibits both wave-like and particle-like properties. Electromagnetic radiation, or radiant energy, is characterized by its wave nature and includes visible light, ultraviolet, infrared, and other types of waves.

• Wavelength (λ): The distance between two adjacent peaks (crests) of a wave. It is usually measured in meters (m), nanometers (nm), or angstroms (Å).

• Frequency (ν): The number of complete wavelengths that pass a given point per second. The unit is hertz (Hz), equivalent to s-1.

• Speed of Light (c): All electromagnetic radiation travels through a vacuum at $c = 3.00 \times 10^8$ m/s.

• Relationship between Wavelength and Frequency: There is an inverse relationship between frequency and wavelength, given by the equation:

$c = \lambda \nu$

• Where $c$ is the speed of light, $\lambda$ is the wavelength, and $\nu$ is the frequency.

• A wave with a high frequency has a short wavelength, and vice versa.

The Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, arranged by wavelength or frequency. The visible region is only a small part of the spectrum, ranging from about 400 nm (violet) to 750 nm (red).

• Order of increasing wavelength: Gamma rays < X-rays < Ultraviolet < Visible < Infrared < Microwaves < Radio waves

• Order of increasing frequency: Radio waves < Microwaves < Infrared < Visible < Ultraviolet < X-rays < Gamma rays

Example Calculations

• Given: Wavelength of sodium lamp light = 589 nm. Find: Frequency ($\nu$).

• Given: FM radio frequency = 89.9 MHz. Find: Wavelength ($\lambda$).

Use $c = \lambda \nu$ to solve for the unknown.

6.2 Quantized Energy and Photons

Classical wave models cannot explain all properties of light. Quantum theory introduces the concept that energy is quantized, meaning it can only be absorbed or emitted in discrete amounts called quanta.

Quantization of Energy (Max Planck)

• Electromagnetic energy can be released or absorbed by atoms only in fixed amounts (quanta).

• The energy of a single quantum is given by:

$E = h \nu$

• $E$ = energy of a quantum (Joules)

• $h$ = Planck's constant ($6.626 \times 10^{-34}$ J·s)

• $\nu$ = frequency (Hz)

• Energy can only be absorbed or emitted in whole-number multiples of $h\nu$ (e.g., $2h\nu$, $3h\nu$).

The Photoelectric Effect and Photons (Albert Einstein)

• When photons (particles of light) of sufficient energy strike a metal surface, they transfer energy to electrons, causing their emission from the metal.

• This demonstrates that light energy is quantized in packets called photons.

• The energy of a photon is:

$E_{\text{photon}} = h \nu$

Example Calculations

• Calculate the energy of one photon of yellow light with a wavelength of 589 nm.

• Calculate the energy of one photon for a laser emitting at a frequency of $4.69 \times 10^{14}$ s-1.

Use $E = h \nu$ or $E = \dfrac{hc}{\lambda}$ as appropriate.

Key Terms

• Electromagnetic radiation: Energy that travels through space as waves.

• Wavelength ($\lambda$): Distance between wave peaks.

• Frequency ($\nu$): Number of waves per second.

• Photon: A quantum of electromagnetic energy.

• Planck's constant ($h$): $6.626 \times 10^{-34}$ J·s.

Example Table: Electromagnetic Spectrum

Type of Radiation	Wavelength Range (m)	Frequency Range (Hz)
Gamma rays	< 10-12	> 1020
X-rays	10-12 – 10-10	1018 – 1020
Ultraviolet	10-10 – 4 × 10-7	1015 – 1017
Visible	4 × 10-7 – 7.5 × 10-7	4 × 1014 – 7.5 × 1014
Infrared	7.5 × 10-7 – 10-3	1011 – 4 × 1014
Microwaves	10-3 – 10-1	109 – 1011
Radio waves	> 10-1	< 109

Example: Calculate the frequency of light with a wavelength of 589 nm:

$\nu = \dfrac{c}{\lambda} = \dfrac{3.00 \times 10^8\ \text{m/s}}{589 \times 10^{-9}\ \text{m}}$

Example: Calculate the energy of a photon with frequency $4.69 \times 10^{14}$ s-1:

$E = h \nu = (6.626 \times 10^{-34}\ \text{J·s})(4.69 \times 10^{14}\ \text{s}^{-1})$

Additional info: Later sections in this chapter will cover atomic spectra, the Bohr model, quantum numbers, and electron configurations, which build on these foundational concepts.