Optical fibers allow the fast transmission of vast amounts of data. In one type of fiber, the wavelength of transmitted light is $1.3 \times 10^3 \mathrm{~nm}$. (a) What is the frequency of the light? (b) Fiber optic cable is available in $12 \mathrm{~km}$ lengths. How long will it take for a signal to travel that distance assuming that the speed of light in the cable is the same as in a vacuum?

A certain cellular telephone transmits at a frequency of $825 \mathrm{MHz}$ and receives at a frequency of $875 \mathrm{MHz}$. (a) What is the wavelength of the transmitted signal in $\mathrm{cm}$ ? (b) What is the wavelength of the received signal in $\mathrm{cm}$ ?

The Balmer equation can be extended beyond the visible portion of the electromagnetic spectrum to include lines in the ultraviolet. What is the wavelength in nanometers of ultraviolet light in the Balmer series when $m=2$ and $n=7$ ?

The MRI (magnetic resonance imaging) body scanners used in hospitals operate with $400 \mathrm{MHz}$ radiofrequency energy. How much energy does this correspond to in kilojoules per mole?

Calculate the energies of the following waves in kilojoules per mole, and tell which member of each pair has the higher value. (a) An FM radio wave at $99.5 \mathrm{MHz}$ and an $\mathrm{AM}$ radio wave at $1150 \mathrm{kHz}$ (b) An $\mathrm{X}$ ray with $\lambda=3.44 \times 10^{-9} \mathrm{~m}$ and a microwave with $\lambda=6.71 \times 10^{-2} \mathrm{~m}$