Waves and Electromagnetic Radiation Notes

Waves and Electromagnetic Radiation

Waves

• This unit explores the physics and phenomena of waves from a chemistry perspective.

• Light waves and electrons exhibit wave-like properties.

• Light waves are electromagnetic phenomena with both electric and magnetic components.

• Light waves propagate through space at the speed of light ($3.0 \times 10^8$ m/s).

• Electromagnetic waves (light waves) have no mass but can exhibit particle-like behavior. These particles of light are called "photons".

Wave Measurements

• Any wave can be mathematically described by wavelength, frequency, and amplitude.

• Wavelength ($\lambda$, "lambda") is the distance between two identical points on a wave in one cycle. The base unit is meters.

• Frequency ($\nu$, "nu") measures the number of wave cycles passing a point in one second. The unit is 1/s or Hertz (Hz).

• Amplitude describes the height or magnitude of the peaks and troughs. For electromagnetic waves, this relates to intensity or brightness.

• The amplitudes of waves will be ignored hereafter.

Electromagnetic Spectrum

• Frequency and wavelength are inversely proportional (as one increases, the other decreases).

• The electromagnetic spectrum includes (from high frequency/short wavelength to low frequency/long wavelength):

  Gummy X-rays Unsee Visible Internal Microwaves Radiowaves

  • Gamma rays

  • X-rays

  • UV

  • Visible Light

  • Infrared

  • Microwaves

  • Radio waves

• Visible light has wavelengths ranging from 400 to 700 nanometers.

• The colors of visible light are red, orange, yellow, green, blue, indigo, and violet.

• Violet has higher frequencies and shorter wavelengths, while red has lower frequencies and longer wavelengths.

• Red light has lower energy than violet light.

• The visible light region progresses from lower energy (red) to higher energy (violet).

ROY G BIV

• Mnemonic for colors of visible light: ROY G BIV (Red, Orange, Yellow, Green, Blue, Indigo, Violet)

• Low Energy → High Energy

• Long Wavelength → Short Wavelength

• Low Frequency → High Frequency

Electromagnetic Radiation

• Relationship between speed, wavelength, and frequency: $u = \lambda \nu$ where: * $u$ is the speed of the wave. * $\lambda$ is the wavelength. * $\nu$ is the frequency.

  • Units: meters x (1/s) = m/s

• The speed of light (c) in a vacuum is a fundamental constant:
  $c = \lambda \nu$
  $c = 3.00 \times 10^8$ m/s

• Assume the electromagnetic wave is traveling in a vacuum unless specified otherwise.

Guided Problem

• A wave with a wavelength of 902 picometers (pm) has a frequency of $5.81 \times 10^7$ Hz. What is the speed of this wave?

  • Known:

    • $\lambda = 902$ pm

    • $\nu = 5.81 \times 10^7$ Hz

  • Unknown:

    • $u$ (speed)

  • Formula:

    • $u = \lambda \nu$

  • Plug in variables:

    • $u = (902 \text{ pm}) \times (5.81 \times 10^7 \text{ Hz}) = 5.24 \times 10^{10} \text{ pm/s}$

  • Conversion to m/s:

    • $5.24 \times 10^{10} \frac{\text{pm}}{\text{s}} \times \frac{1 \times 10^{-12} \text{ m}}{1 \text{ pm}} = 5.24 \times 10^{-2} \frac{\text{m}}{\text{s}}$

  • Alternative method:

    • Convert wavelength to meters first:
      $902 \text{ pm} \times \frac{1 \times 10^{-12} \text{ m}}{1 \text{ pm}} = 9.02 \times 10^{-10} \text{ m}$

    • Then calculate speed:
      $(9.02 \times 10^{-10} \text{ m}) \times (5.81 \times 10^7 \text{ Hz}) = 5.24 \times 10^{-2} \frac{\text{m}}{\text{s}}$

Planck's Constant

• Max Planck observed that electromagnetic radiation energy is emitted or absorbed in discrete bits called photons.
  $E = h\nu$
  where:
  * E is the energy of one photon of light (in Joules, J).
  * $h$ is Planck's constant = $6.63 \times 10^{-34}$ J⋅s
  * $\nu$ is the frequency.

• The energy of a photon changes with its frequency.

• Higher frequency photons have higher energy.

• An atom can absorb a photon if the energy (frequency) is just right.

• When an atom absorbs a photon, an electron is promoted to a higher energy state (excited state).

• When the excited electron releases energy, it emits a photon.

• After releasing a photon, the electron returns to a lower energy state ("relaxed").