Lecture Notes: Wavelength and Frequency of Photons

Key Equations and Concepts

• Speed of light (C):

  • Constant value: (3 \times 10^8) meters per second (m/s).

• Wavelength (λ) and Frequency (ν) Relationship:

  • Equation: (C = \lambda \times \nu)
  • Wavelength (λ): Measured in meters.
  • Frequency (ν): Measured in hertz (Hz).

Conversion Principles

• Micrometers to Meters:

  • 1 micrometer = (10^{-6}) meters.
  • Conversion example: (1.2 \times 10^{-4}) m = 120 micrometers.

• Nanometers to Meters:

  • 1 nanometer = (10^{-9}) meters.
  • Replace nanometers with (10^{-9}) m for calculation.

• Megahertz to Hertz:

  • 1 megahertz = (10^6) hertz.
  • Example: 95 MHz = 95 (\times 10^6) Hz.

Problem Examples

Problem 1: Calculate Wavelength from Frequency

1. Given: Frequency = (2.5 \times 10^{12}) Hz.
2. Calculate Wavelength:
   • Formula: (\lambda = \frac{C}{\nu})
   • Result: (1.2 \times 10^{-4}) m or 120 micrometers.

Problem 2: Calculate Frequency from Wavelength

1. Given: Wavelength = (1.5 \times 10^{-8}) m.
2. Calculate Frequency:
   • Formula: (\nu = \frac{C}{\lambda})
   • Result: (2 \times 10^{16}) Hz.

Problem 3: Convert Wavelength and Calculate Frequency

1. Given: Wavelength = 350 nanometers.
2. Convert Wavelength: 350 nm = 350 (\times 10^{-9}) m.
3. Calculate Frequency:
   • Result: (8.57 \times 10^{14}) Hz.

Problem 4: Calculate Wavelength for Frequency in Megahertz

1. Given: Frequency = 95 MHz.
2. Convert Frequency: 95 (\times 10^6) Hz.
3. Calculate Wavelength:
   • Result: 3.16 m.

Frequency and Wavelength Relationship

• Inversely related:
  • As frequency increases, wavelength decreases.
  • As wavelength increases, frequency decreases.

Energy and Frequency Relationship

• Planck’s Constant (H):
  • Value: 6.626 (\times 10^{-34}) joules (\times) seconds.
• Equation:
  • (E = h \times \nu)
  • Frequency (\nu = \frac{E}{h})

Problem 5: Calculate Frequency from Energy

1. Given: Energy = (3.5 \times 10^{-18}) joules.
2. Calculate Frequency:
   • Result: (5.28 \times 10^{15}) Hz.

Problem 6: Calculate Wavelength from Energy

1. Given: Energy = (4.3 \times 10^{-19}) joules.
2. Calculate Frequency:
   • Result: (6.49 \times 10^{14}) Hz.
3. Calculate Wavelength:
   • Result: (4.62 \times 10^{-7}) m.
4. Convert to Nanometers:
   • Result: 462 nm.

Conclusion

• Understanding the relationship between wavelength, frequency, and energy is crucial for solving photon-related problems.
• Familiarity with unit conversions (micrometers, nanometers, megahertz) is important for calculations.