Taking into account the definition of wavelength, frecuency and propagation speed, the wavelength of light with a frequency of 2.04×10¹⁵ Hz is 147.06 nm.
<h3>Definition of wavelength </h3>
The wavelength is the minimum distance between two successive points of the wave from which the wave repeats itself.It is expressed in units of length (m).
<h3>Definition of frequency</h3>
Frequency is the number of vibrations that occur in a unit of time. Its unit is s⁻¹ or hertz (Hz).
<h3>Definition of propagation speed</h3>
The propagation speed of a wave can be measured as the time that elapses between when it is emitted and when it is received. In other words, the speed of propagation of a wave is the magnitude that measures the speed at which the disturbance of the wave propagates along its displacement.
The propagation speed relate the wavelength (λ) and the frequency (f) inversely proportional using the following equation:
v = f×λ
All electromagnetic waves propagate in a vacuum at a constant speed of 3×10⁸ m/s, the speed of light.
<h3>Wavelength in nanometers</h3>
In this case, you know:
- v=3×10⁸ m/s
- f= 2.04×10¹⁵ Hz
- λ= ?
Replacing in the definition of propagation speed:
3×10⁸ m/s= 2.04×10¹⁵ Hz× λ
Solving:
λ= 3×10⁸ m/s ÷ 2.04×10¹⁵ Hz
<u><em>λ= 1.4706×10⁻⁷ m= 147.06 nm</em></u> (being 10⁻⁹ m= 1 nm)
In summary, the wavelength of the wave is 147.06 nm.
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