Answer:
The wavelength of the wave is 2.34 nm.
Explanation:
It is required to find the wavelength of a [tex]1.28\times 10^{17}\ Hz[/tex] wave. A wave moves with a speed of light. Speed of a wave is given in terms of wavelength and frequency. So,
[tex]v=f\lambda[/tex]
[tex]\lambda=\dfrac{c}{f}\\\\\lambda=\dfrac{3\times 10^8}{1.28\times 10^{17}}\\\\\lambda=2.34\times 10^{-9}\ m\\\\\text{or}\\\\\lambda=2.34\ nm[/tex]
So, the wavelength of the wave is 2.34 nm.
The wavelength of the wave is 2.34 × 10⁻⁹ meters.
Given the data in the question;
Wavelength; [tex]\lambda =\ ?[/tex]
To determine the wavelength of the wave, we use the expression for the relations between wavelength, frequency and speed of light.
[tex]\lambda = \frac{c}{f}[/tex]
Where [tex]\lambda[/tex] is wavelength, f is frequency and c is speed of light ( [tex]3*10^8m/s[/tex] )
We substitute our values into the equation
[tex]\lambda = \frac{3*10^8m/s}{1.28*10^{17}Hz} \\\\\lambda = \frac{3*10^8m/s}{1.28*10^{17}s^{-1}} \\\\\lambda = 2.34 * 10^{-9}m[/tex]
Therefore, the wavelength of the wave is 2.34 × 10⁻⁹ meters.
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