We know that the energy of electromagnetic radiation is given by:
[tex]E=hf[/tex]where E is the energy, h is Planck's constant and f is the frequency. Before we can use this formula we need to convert the amount of energy given to J so let's do that:
[tex]1.08\text{ }\frac{J}{mol}\cdot\frac{1\text{ mol}}{6.022\times10^{23}}=1.793\times10^{-24}J[/tex]Now that we have the energy of the radiation, we plug it on the energy equation and solve for the frequency:
[tex]\begin{gathered} 1.793\times10^{-24}=6.63^\times10^{-34}f \\ f=\frac{1.793\times10^{-24}}{6.63\times10^{-34}} \\ f=2.704\times10^9 \end{gathered}[/tex]Therefore, the frequency of the cell phone electromagnetic radiation is:
[tex]2.704\times10^9\text{ Hz}[/tex]Now that we know the frequency we just need to remember that the frequency and wavelength of electromagnetic radiation are related by:
[tex]\lambda=\frac{c}{f}[/tex]Then we have:
[tex]\begin{gathered} \lambda=\frac{3\times10^8}{2.704\times10^9} \\ \lambda=0.111 \end{gathered}[/tex]Therefore, the wavelength is 0.111 m
