Answer
a. UVA frequencies range from $7.50\times10^{14}Hz$ to $9.38\times10^{14}Hz$.
UVB frequencies range from $9.38\times10^{14}Hz$ to $1.07\times10^{15}Hz$.
b. UVA wavenumbers range from $1.57\times10^{7} m^{-1}$ to $1.96\times10^{7} m^{-1}$.
UVB wavenumbers range from $1.96\times10^{7} m^{-1}$ to $2.24\times10^{7} m^{-1}$.
Work Step by Step
Start with frequencies.
$$f=\frac{c}{\lambda}=\frac{3.00\times10^{8}m/s}{400\times10^{-9}m}=7.50\times10^{14}Hz$$
$$f=\frac{c}{\lambda}=\frac{3.00\times10^{8}m/s}{320\times10^{-9}m}=9.38\times10^{14}Hz$$
$$f=\frac{c}{\lambda}=\frac{3.00\times10^{8}m/s}{320\times10^{-9}m}=1.07\times10^{15}Hz$$
We see that UVA frequencies range from $7.50\times10^{14}Hz$ to $9.38\times10^{14}Hz$.
We see that UVB frequencies range from $9.38\times10^{14}Hz$ to $1.07\times10^{15}Hz$.
On to wavenumbers.
$$k=\frac{2 \pi}{\lambda}=\frac{2 \pi}{400\times10^{-9}m}=1.57\times10^{7} m^{-1}$$
$$k=\frac{2 \pi}{\lambda}=\frac{2 \pi}{320\times10^{-9}m}=1.96\times10^{7} m^{-1}$$
$$k=\frac{2 \pi}{\lambda}=\frac{2 \pi}{280\times10^{-9}m}=2.24\times10^{7} m^{-1}$$
We see that UVA wavenumbers range from $1.57\times10^{7} m^{-1}$ to $1.96\times10^{7} m^{-1}$.
We see that UVB wavenumbers range from $1.96\times10^{7} m^{-1}$ to $2.24\times10^{7} m^{-1}$.
