Wavelength and Frequency in Light

Key Concepts and Definitions

  • Speed of Light (C): A constant value that represents the speed at which light travels in a vacuum, approximately C=3.0imes108extm/sC = 3.0 imes 10^8 ext{ m/s}.

  • Frequency (V): The number of cycles of a wave that occur per second, measured in hertz (Hz) or exts−1ext{s}^{-1}.

  • Wavelength (( \lambda )): The distance between successive crests of a wave, commonly measured in meters (m) or nanometers (nm). Typically, it is expressed in nanometers for light waves.

  • Relationship: The equation relating speed, frequency, and wavelength is:
    extC=λ×Vext{C} = \lambda \times V
    Rearranging gives:
    λ=CV\lambda = \frac{C}{V}

Example Problem 1: Finding Wavelength from Frequency

  • Given: Frequency V=7.26imes1014extHzV = 7.26 imes 10^{14} ext{ Hz} (violet region)

    • Task: Find wavelength λ\lambda.

  • Calculation:

    1. Use the formula: λ=CV\lambda = \frac{C}{V}
    2. Substitute the values:
    • λ=3.0imes108extm/s7.26imes1014extHz\lambda = \frac{3.0 imes 10^8 ext{ m/s}}{7.26 imes 10^{14} ext{ Hz}}
    • λ=4.13imes10−7extm\lambda = 4.13 imes 10^{-7} ext{ m}

  • Conversion to Nanometers:

    • To convert from meters to nanometers:
    • Multiply by 10910^9:
      λ=4.13imes10−7extm×109extnm1extm=4,113extnm\lambda = 4.13 imes 10^{-7} ext{ m} \times \frac{10^9 ext{ nm}}{1 ext{ m}} = 4,113 ext{ nm}

Example Problem 2: Calculating Wavelength from Frequency

  • Given: Frequency V=5.00imes1014extHzV = 5.00 imes 10^{14} ext{ Hz}

    • Task: Find wavelength λ\lambda.

  • Calculation:

    1. Use the same formula:
    • λ=CV\lambda = \frac{C}{V}
    1. Substitute the values:
    • λ=3.0imes108extm/s5.00imes1014extHz\lambda = \frac{3.0 imes 10^8 ext{ m/s}}{5.00 imes 10^{14} ext{ Hz}}
    • λ=6.0imes10−7extm\lambda = 6.0 imes 10^{-7} ext{ m}

  • Conversion to Nanometers:

    • Convert meters to nanometers:
    • λ=6.0imes10−7extm×109extnm1extm=600extnm\lambda = 6.0 imes 10^{-7} ext{ m} \times \frac{10^9 ext{ nm}}{1 ext{ m}} = 600 ext{ nm}

Conclusion

  • The relationship between wavelength and frequency is a crucial concept in understanding electromagnetic radiation.
  • Mastery of the speed, frequency, and wavelength calculations is essential for further studies in physics and chemistry, especially in optics and wave mechanics.