Answer
See explanation.
Work Step by Step
Electromagnetic waves move through air at essentially the speed of light in vacuum.
a, i.
$$f=\frac{c}{\lambda}=\frac{3.00\times10^{8}m/s}{5.0\times10^{3}m}=6.0\times10^{4}Hz$$
a, ii.
$$f=\frac{c}{\lambda}=\frac{3.00\times10^{8}m/s}{5.0\times10^{-6}m}=6.0\times10^{13}Hz$$
a, iii.
$$f=\frac{c}{\lambda}=\frac{3.00\times10^{8}m/s}{5.0\times10^{-9}m}=6.0\times10^{16}Hz$$
b, i.
$$\lambda =\frac{c}{f}=\frac{3.00\times10^{8}m/s}{6.50\times10^{21}Hz }= 4.62\times10^{-14}m=4.62\times10^{-5}nm $$
b, ii.
$$\lambda =\frac{c}{f}=\frac{3.00\times10^{8}m/s}{590\times10^{3}Hz }= 508m=5.08\times10^{11}nm $$
