Example 6.2: Calculating the Energy of Radiation
Calculating the Energy of Radiation
When we see light from a neon sign, we are observing radiation from excited neon atoms. If this radiation has a wavelength of
640 nm, what is the energy of the photon being emitted?
Solution
\(λ_{\mathrm{neon}}\) \(= 640\ \mathrm{nm}\)
\(E_{\mathrm{photon}}\) = ?
We use the version of Planck's equation that includes the wavelength,
λ.
\(E = \dfrac{h_{\mathrm{Planck}} \cdot c_{\mathrm{0}}}{λ}\)
\(h_{\mathrm{Planck}}\) \(= 6.626\times 10^{-34}\ \mathrm{J}\ \mathrm{s}\)
\(E_{\mathrm{photon}}\) \(= \dfrac{h_{\mathrm{Planck}} \cdot c_{\mathrm{0}}}{λ_{\mathrm{neon}}}\)
\(\ \ \ =\dfrac{6.626\times 10^{-34}\ \mathrm{J}\ \mathrm{s} \cdot 2.998\times 10^{8}\ \frac{\mathrm{m}}{\mathrm{s}}}{640\ \mathrm{nm}}\)
\(\ \ \ =\dfrac{1.98647\times 10^{-25}\ \mathrm{J}\ \mathrm{m}}{640\ \mathrm{nm}}\)
\(\ \ \ =3.104\times 10^{-19}\ \mathrm{J}\)