Understanding the Relationship

The relationship between the wavelength (λ), frequency (ν), and the speed of light (c) is given by the following equation:

c = λν

* c: Speed of light in a vacuum (approximately 3 x 10⁸ meters per second)

* λ: Wavelength (measured in meters)

* ν: Frequency (measured in Hertz, or cycles per second)

Calculation

1. Rearrange the equation to solve for wavelength:

λ = c / ν

2. Plug in the values:

λ = (3 x 10⁸ m/s) / (6.82 x 10¹⁴ Hz)

3. Calculate:

λ ≈ 4.39 x 10⁻⁷ meters

Converting to Nanometers (nm):

Wavelength is often expressed in nanometers. To convert meters to nanometers, multiply by 10⁹:

4.39 x 10⁻⁷ meters * (10⁹ nm / 1 meter) = 439 nm

Answer:

The wavelength of blue light with a frequency of 6.82 x 10¹⁴ Hz is approximately 439 nanometers.