Introduction to Spectrochemical Methods

Question

Calculate the wavelength and the energy in joules associated with a signal at 220 MHz.

Answer 1

Calculate the wavelength and the energy in joules associated with a signal at 220 MHz.

To calculate the wavelength, we use

c = λν

c = speed of light = 3x10⁸ m/s

λ = wavelength = ?

ν = frequency = 220 MHz x 1x10⁶ Hz / MHz = 2.20x10⁸ Hz= 2.20x10⁸ s^-1

Solving for λ, we have...

λ = c / ν = 3x10⁸ m/s / 2.20x10⁸ s^-1

λ = 1.36 m (meters)

To calculate the energy associated with this frequency, we use

E = hν

E = energy = ?

h = Plank's constant = 6.626x10^-34 Js

ν = frequency in Hz (s^-1) = 2.20x10⁸ s^-1

Solving for E, we have...

E = (6.626x10^-34 Js)(2.20x10⁸ s^-1)

E = 1.46x10^-25 J

Answer 2

For the first part of this question you should use the equation f = v / λ where f is the frequency given in Hz, v is speed in this case the speed of light, and lambda is wavelength in nanometers. For the second part you use the equation E = hc / λ where E is energy, h is plank’s constant and c is the speed of light.