Given that,
The wavelength of microwave radiation = 1 cm = 0.01 m
To find,
The frequency and the energy of a single photon of this radiation.
Solution,
Let f be the frequency of the wave. The relation between frequency and wavelength is given by :
[tex]f=\dfrac{c}{\lambda}\\\\f=\dfrac{3\times 10^8}{0.01}\\\\=3\times 10^{10}\ Hz[/tex]
Let E be the energy of the wave. The energy of the wave is given by :
[tex]E=hf\\\\=6.63\times 10^{-34}\times 3\times 10^{10}\\\\=1.98\times 10^{-23}\ J[/tex]
We know that, [tex]N_A=6.022\times 10^{23}\ \text{photons/mol}[/tex]
Energy :
[tex]E={1.98\times 10^{-23}}\times {6.023\times 10^{23}}\\\\=11.92\ J/mol[/tex]
Hence, this is the required solution.
