Question

Cell phones use electromagnetic radiation with energy of about 1.08J/mol photons. Calculate the wavelength and frequency that can be used to describe light with this energy.

Answer 1

We know that the energy of electromagnetic radiation is given by:

`E=hf`

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:

`1.08\text{ }(J)/(mol)\cdot\frac{1\text{ mol}}{6.022*10^(23)}=1.793*10^(-24)J`

Now that we have the energy of the radiation, we plug it on the energy equation and solve for the frequency:

`\begin{gathered} 1.793*10^(-24)=6.63^*10^(-34)f \\ f=(1.793*10^(-24))/(6.63*10^(-34)) \\ f=2.704*10^9 \end{gathered}`

Therefore, the frequency of the cell phone electromagnetic radiation is:

`2.704*10^9\text{ Hz}`

Now that we know the frequency we just need to remember that the frequency and wavelength of electromagnetic radiation are related by:

`\lambda=(c)/(f)`

Then we have:

`\begin{gathered} \lambda=(3*10^8)/(2.704*10^9) \\ \lambda=0.111 \end{gathered}`

Therefore, the wavelength is 0.111 m