Question

Microwave radiation has a wavelength on the order of 1.0 cm. Calculate the frequency and the energy of a single photon of this radiation. Calculate the energy of an Avogadro's number of photons (called as einstein) of this radiation.

Answer 1

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 :

`f=(c)/(\lambda)\\\\f=(3* 10^8)/(0.01)\\\\=3* 10^(10)\ Hz`

Let E be the energy of the wave. The energy of the wave is given by :

`E=hf\\\\=6.63* 10^(-34)* 3* 10^(10)\\\\=1.98* 10^(-23)\ J`

We know that,
`N_A=6.022* 10^(23)\ \text{photons/mol}`

Energy :

`E={1.98* 10^(-23)}* {6.023* 10^(23)}\\\\=11.92\ J/mol`

Hence, this is the required solution.