Respuesta :
Answer: The frequency of the radiation is 33.9 THz
Explanation:
We are given:
Wave number of the radiation, [tex]\bar{\nu}=1130cm^{-1}[/tex]
Wave number is defined as the number of wavelengths per unit length.
Mathematically,
[tex]\bar{\nu}=\frac{1}{\lambda}[/tex]
where,
[tex]\bar{\nu}[/tex] = wave number = [tex]1130cm^{-1}[/tex]
[tex]\lambda[/tex] = wavelength of the radiation = ?
Putting values in above equation, we get:
[tex]1130cm^{-1}=\farc{1}{\lambda}\\\\\lambda=\frac{1}{1130cm^{-1}}=8.850\times 10^{-4}cm[/tex]
Converting this into meters, we use the conversion factor:
1 m = 100 cm
So, [tex]8.850\times 10^{-4}cm=8.850\times 10^{-4}\times 10^{-2}=8.850\times 10^{-6}m[/tex]
- The relation between frequency and wavelength is given as:
[tex]\nu=\frac{c}{\lambda}[/tex]
where,
c = the speed of light = [tex]3\times 10^8m/s[/tex]
[tex]\nu[/tex] = frequency of the radiation = ?
Putting values in above equation, we get:
[tex]\nu=\frac{3\times 10^8m/s}{8.850\times 10^{-4}m}[/tex]
[tex]\nu=0.339\times 10^{14}Hz[/tex]
Converting this into tera Hertz, we use the conversion factor:
[tex]1THz=1\times 10^{12}Hz[/tex]
So, [tex]0.339\times 10^{14}Hz\times \frac{1THz}{1\times 10^{12}Hz}=33.9THz[/tex]
Hence, the frequency of the radiation is 33.9 THz
