Question

calculate the frequency in hertz of electromagnetic radiation that has a wavelength of 720.0 nm. (c = 3.00 x 10⁸ m/s)

Answer 1

Considering the definition of wavelenght, frecuency and propagation speed,  the frequency of the electromagnetic radiation that has a wavelength of 720.0 nm is 4.167×10¹⁴ Hz.

In a periodic wave the wavelength (λ) is the physical distance between two points from which the wave repeats itself. It is expressed in units of length (m).

The frequency (f) is a measure of the number of cycles or repetitions of the wave per unit of time. Its unit is s⁻¹ or hertz (Hz).

The propagation speed is the speed with which the wave propagates in the medium, that is, it is the magnitude that measures the speed at which the wave's disturbance propagates along its displacement. Relate the wavelength (λ) and the frequency (f) inversely proportional using the following equation:

v = f×λ

In this case, you know:

• v=c= 3×10⁸ m/s
• f= ?
• λ= 720 nm= 720×10⁻⁹ m

Replacing in the definition of propagation speed:

3×10⁸ m/s= f × 720×10⁻⁹ m

Solving:

3×10⁸ m/s÷ 720×10⁻⁹ m= f

4.167×10¹⁴ Hz= f

Finally, the frequency of the electromagnetic radiation that has a wavelength of 720.0 nm is 4.167×10¹⁴ Hz.

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