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. How to calculate the energy of an Avogadro’s number of photons (called an einstein) of this radiation ?

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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. How to calculate the energy of an Avogadro’s number of photons (called an einstein) of this radiation ?

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Answer 1 · 2015-04-08T22:05:33

If wavelength is $λ = 1 c m = 0.01 m$ $lambda=1 cm=0.01m$
Frequency is: $ν = \frac{c}{λ} = \frac{3 \times 10^{8}}{0.01} = 3 \times 10^{10} H z$ $nu=c/lambda=(3xx10^8)/0.01=3xx10^10Hz$

Energy of one photon of this frequency will be (From Einstein's relationship):
$E = h \cdot ν = 6.63 \times 10^{- 34} \cdot 3 \times 10^{10} ≅ 2 \times 10^{- 23} J$ $E=h*nu=6.63xx10^(-34)*3xx10^10~=2xx10^-23J$

(Where $c$ $c$ is the speed of light and $h$ $h$ is Plank's Constant)

Now using $N_{A} = 6.022 \times 10^{23} m o l^{- 1}$ $N_A=6.022xx10^23 mol^-1$ you can find the energy you need!

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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. How to calculate the energy of an Avogadro’s number of photons (called an einstein) of this radiation ?

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