Electromagnetic Radiation, Quantum Effects, and Atomic Structure: General Chemistry Study Notes

Electromagnetic Radiation and the Electromagnetic Spectrum

Overview of Electromagnetic Radiation

Electromagnetic radiation is a form of energy that travels through space as waves and includes a wide range of wavelengths and frequencies. The electromagnetic spectrum encompasses all types of electromagnetic radiation, from radio waves to gamma rays.

• Electromagnetic Spectrum: A continuum of electromagnetic radiation containing all wavelengths and frequencies.

• Wavelength (λ): The distance between two consecutive crests or troughs of a wave. Measured in meters (m), nanometers (nm), or picometers (pm).

• Frequency (ν): The number of wave cycles passing a point per second. Measured in Hertz (Hz), or s-1.

• Amplitude: The height of a wave from its origin to its crest or trough.

Electromagnetic Spectrum Classification

The electromagnetic spectrum is divided into regions based on wavelength and frequency:

Type	Wavelength Range	Frequency Range	Energy
Radio Waves	103 - 10-1 m	104 - 108 Hz	Lowest
Microwave	10-1 - 10-3 m	108 - 1011 Hz	Low
Infrared	10-3 - 10-6 m	1011 - 1014 Hz	Medium
Visible Light	400 - 700 nm	~1014 - 1015 Hz	Medium-high
Ultraviolet	10-7 - 10-8 m	1015 - 1016 Hz	High
X-rays	10-8 - 10-11 m	1016 - 1019 Hz	Very high
Gamma Rays	<10-11 m	>1019 Hz	Highest

Additional info: Table ranges inferred from standard chemistry sources.

Visible Light Spectrum

The visible light spectrum is the portion of the electromagnetic spectrum that can be seen by the human eye, ranging from approximately 400 nm (violet) to 700 nm (red).

• Colors: Red, Orange, Yellow, Green, Blue, Violet (ROYGBV)

• Wavelengths: Red (~700 nm), Violet (~400 nm)

Relationship Between Wavelength and Frequency

At a fixed speed, the frequency of light is inversely proportional to its wavelength:

• Shorter wavelengths correspond to higher frequencies.

• Longer wavelengths correspond to lower frequencies.

Speed of Light and Related Calculations

Speed of Light Formula

The speed of light in a vacuum is a physical constant, denoted as c:

• Speed of Light (c): $c = 3.00 \times 10^8$ m/s

• Formula: $c = \lambda \nu$

• $\lambda$ = wavelength in meters

• $\nu$ = frequency in s-1 (Hz)

Example Calculation

• Calculate frequency: For red light with a wavelength of 663.8 nm:

• Convert nm to m: $663.8 \text{ nm} = 6.638 \times 10^{-7} \text{ m}$

• Use $c = \lambda \nu$ to solve for $\nu$.

Atomic Emission and Element Identification

Emission Spectra

When elements are burned, they emit light at specific wavelengths, which can be used to identify them.

Element	Wavelength (nm)
Ag	328.1
Ba	455.4
Cu	324.8
Na	589.6

Photon Energy and Quantum Theory

Planck's Quantum Theory

Max Planck and Albert Einstein proposed that light consists of discrete packets of energy called photons or quanta.

• Photon: A particle of light energy.

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

Photon Energy Formulas

• Energy from frequency: $E = h \nu$

• Energy from wavelength: $E = \frac{hc}{\lambda}$

Additional info: These formulas show energy is directly proportional to frequency and inversely proportional to wavelength.

Moles and Energy

• To find the energy for a mole of photons, multiply by Avogadro's number ($6.022 \times 10^{23}$ photons/mol).

Photoelectric Effect

Einstein's Photoelectric Effect

When light of sufficient energy strikes a metal surface, electrons can be ejected. The minimum energy required to remove an electron is called the binding energy or work function ($E_{BE}$).

• Photoelectric Effect Formula: $E_{\text{photon}} = E_{BE} + E_{KE}$

• $E_{KE}$ = kinetic energy of the ejected electron

• 1 electronvolt (eV) = $1.602 \times 10^{-19}$ J

Example Calculation

• Given photon energy and binding energy, calculate kinetic energy: $E_{KE} = E_{\text{photon}} - E_{BE}$

De Broglie Wavelength

Wave-Particle Duality

Louis de Broglie proposed that all matter has wave-like properties. The wavelength of a moving object is given by:

• De Broglie Wavelength Formula: $\lambda = \frac{h}{mv}$

• $m$ = mass of object (kg)

• $v$ = velocity (m/s)

Additional info: Formula applies to all matter, but is most significant for small particles like electrons.

Heisenberg Uncertainty Principle

Uncertainty in Measurement

Werner Heisenberg stated that it is impossible to simultaneously know both the exact position and momentum (or velocity) of a particle, such as an electron.

• Uncertainty Principle Formula: $\Delta x \cdot \Delta p \geq \frac{h}{4\pi}$

• $\Delta x$ = uncertainty in position (m)

• $\Delta p$ = uncertainty in momentum (kg·m/s)

• Momentum: $p = mv$

Example Calculation

• Given uncertainty in position, calculate uncertainty in velocity: $\Delta v = \frac{h}{4\pi m \Delta x}$

Summary Table: Key Equations

Concept	Equation (LaTeX)	Variables
Speed of Light	$c = \lambda \nu$	c = speed of light, λ = wavelength, ν = frequency
Photon Energy (frequency)	$E = h \nu$	h = Planck's constant, ν = frequency
Photon Energy (wavelength)	$E = \frac{hc}{\lambda}$	h = Planck's constant, c = speed of light, λ = wavelength
Photoelectric Effect	$E_{\text{photon}} = E_{BE} + E_{KE}$	$E_{BE}$ = binding energy, $E_{KE}$ = kinetic energy
De Broglie Wavelength	$\lambda = \frac{h}{mv}$	h = Planck's constant, m = mass, v = velocity
Heisenberg Uncertainty Principle	$\Delta x \cdot \Delta p \geq \frac{h}{4\pi}$	$\Delta x$ = uncertainty in position, $\Delta p$ = uncertainty in momentum

Key Points and Applications

• Electromagnetic radiation includes visible light, radio waves, microwaves, infrared, ultraviolet, X-rays, and gamma rays.

• Energy of electromagnetic radiation increases with frequency and decreases with wavelength.

• Photoelectric effect demonstrates the particle nature of light and is used to determine work functions of metals.

• De Broglie wavelength shows that matter has wave-like properties, especially significant for small particles.

• Heisenberg uncertainty principle sets fundamental limits on measurement precision for quantum particles.

Examples and Practice Problems

• Calculate frequency from wavelength: Use $c = \lambda \nu$.

• Identify element from emission wavelength: Compare measured wavelength to standard values.

• Calculate photon energy: Use $E = h \nu$ or $E = \frac{hc}{\lambda}$.

• Photoelectric effect calculations: Find kinetic energy or work function using $E_{\text{photon}} = E_{BE} + E_{KE}$.

• De Broglie wavelength: Calculate wavelength for a moving particle using $\lambda = \frac{h}{mv}$.

• Uncertainty principle: Calculate uncertainty in position or velocity using $\Delta x \cdot \Delta p \geq \frac{h}{4\pi}$.

Additional info: All equations and relationships are standard in introductory college-level General Chemistry.