Answer:
(a) UVA - frequency range: 7.5*10^14 Hz to 9.37*10^14 Hz
UVB - frequency range: 9.37*10^14Hz to 1.07*10^15Hz
(b) UVA - wavenumber range: 1.57*10^7 m^-1 to 1.96*10^7m^-1
UVB - wavenumber range: 1.97*10^7 m^-1 to 2.24*10^7m^-1
Explanation:
In order to calculate the frequency ranges fro the two categories of ultraviolet light, you use the following formula:
[tex]f=\frac{c}{\lambda}[/tex] (1)
f: frequency
c: speed of light in vacuum = 3*10^8 m/s
λ: wavelength
(a) For UVA the wavelength range is λ1 = 320nm to λ2 = 400nm.
The frequency range is:
[tex]f_1=\frac{c}{\lambda_1}=\frac{3*10^8m/s}{320*10^{-9}m}=9.37*10^{14}Hz\\\\f_2=\frac{c}{\lambda_2}=\frac{3*10^8m/s}{400*10^{-9}m}=7.5*10^{14}Hz[/tex]
frequency range: 7.5*10^14 Hz to 9.37*10^14 Hz
For UVB the wavelength range is λ1 = 280nm to λ2 = 320nm.
The frequency range is:
[tex]f_1=\frac{3*10^8m/s}{280*10^{-9}m}=1.07*10^{15}Hz\\\\f_2=\frac{3*10^8m/s}{320*10^{-9}m}=9.37*10^{14}Hz\\\\[/tex]
frequency range: 9.37*10^14Hz to 1.07*10^15Hz
(b) The ranges for the wavenumbers are:
UVA:
[tex]k_1=\frac{2\pi}{\lambda_1}=\frac{2\pi}{320*10^{-9}m}=1.96*10^7m^{-1}\\\\k_2=\frac{2\pi}{\lambda_2}=\frac{2\pi}{400*10^{-9}m}=1.57*10^7m^{-1}[/tex]
wavenumber range: 1.57*10^7 m^-1 to 1.96*10^7m^-1
UVB:
[tex]k_1=\frac{2\pi}{280*10^{-9}m}=2.24*10^7m^{-1}\\\\k_2=\frac{2\pi}{320*10^{-9}m}=1.96*10^7m^{-1}[/tex]
wavenumber range: 1.97*10^7 m^-1 to 2.24*10^7m^-1
