Taking into account the definition of wavelength, frecuency and propagation speed, the frequency of radiation whose wavelength is 0.80 nm is 3.75×10¹⁷ s⁻¹.
First of all, wavelength (λ) is the minimum distance between two successive points on the wave that are in the same state of vibration. It is expressed in units of length (m).
On the other side, frequency (f) is the number of vibrations that occur in a 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. The propagation speed relates the wavelength (λ) and the frequency (f) by:
v=f× λ
Electromagnetic waves propagate in a vacuum at a constant speed of 3×10⁸ m/s, the speed of light. Due to the little difference that exists between the speed of propagation in a vacuum and in air, it is considered that in air they propagate at that speed as well.
So, in this case, you know:
Replacing in the expresion for propagation speed:
3×10⁸ m/s= f× 0.80×10⁻⁹ m
Solvign:
f= 3×10⁸ m/s÷ 0.80×10⁻⁹ m
f= 3.75×10¹⁷ s⁻¹
Finally, the frequency of radiation whose wavelength is 0.80 nm is 3.75×10¹⁷ s⁻¹.
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