Wavelength and Frequency in Light

Speed of Light (C): A constant value that represents the speed at which light travels in a vacuum, approximately C = 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 ext{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:
ext{C} = \lambda \times V
Rearranging gives:
\lambda = \frac{C}{V}

Given: Frequency V = 7.26 imes 10^{14} ext{ Hz} (violet region)
- Task: Find wavelength \lambda.
Calculation:
1. Use the formula: \lambda = \frac{C}{V}
2. Substitute the values:
- \lambda = \frac{3.0 imes 10^8 ext{ m/s}}{7.26 imes 10^{14} ext{ Hz}}
- \lambda = 4.13 imes 10^{-7} ext{ m}
Conversion to Nanometers:
- To convert from meters to nanometers:
- Multiply by 10^9:
  \lambda = 4.13 imes 10^{-7} ext{ m} \times \frac{10^9 ext{ nm}}{1 ext{ m}} = 4,113 ext{ nm}

Given: Frequency V = 5.00 imes 10^{14} ext{ Hz}
- Task: Find wavelength \lambda.
Calculation:
1. Use the same formula:
- \lambda = \frac{C}{V}
1. Substitute the values:
- \lambda = \frac{3.0 imes 10^8 ext{ m/s}}{5.00 imes 10^{14} ext{ Hz}}
- \lambda = 6.0 imes 10^{-7} ext{ m}
Conversion to Nanometers:
- Convert meters to nanometers:
- \lambda = 6.0 imes 10^{-7} ext{ m} \times \frac{10^9 ext{ nm}}{1 ext{ m}} = 600 ext{ nm}

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.