Question

Calculate the frequency (Hz), wavelength$\left({\mathrm{cm}}^{-1}\right)$, and energy (J/photon and J/mols of photon]) of visible light with a wavelength of 562 nm.

Short answer

The answer to the above question is,

(a).The frequency is$\mathrm{v}=5.34.{10}^{14}\mathrm{hz}\tilde{\mathrm{v}}$

(b).The wavenumber is$\tilde{\mathrm{v}}=1.78.{10}^4{\mathrm{cm}}^{-1}$

(c). The energy is$\mathrm{E}=213075\mathrm{J}/\mathrm{mol}$

Step-by-step solution

Calculate frequency:

$$\begin{gathered} \mathrm{v}=\frac{\mathrm{c}}{\mathrm{\lambda }} \\ =\frac{3.{10}^8\mathrm{m}/{\mathrm{S}}^2}{562.{10}^{-9}\mathrm{m}} \\ \mathrm{v}=5.34.{10}^{14}\mathrm{Hz} \end{gathered}$$

Calculate wavenumber:

$$\begin{gathered} \tilde{\mathrm{v}}=\frac{1}{\mathrm{\lambda }} \\ =\frac{1}{562.{10}^{-9}\mathrm{m}} \\ \tilde{\mathrm{v}}=1.78.{10}^6{\mathrm{m}}^{-1} \\ \tilde{\mathrm{v}}=1.78.{10}^4{\mathrm{cm}}^{-1} \end{gathered}$$

Calculate Energy:

$$\begin{gathered} \mathrm{E}=\mathrm{h}.\mathrm{v} \\ =6.626.{10}^{-34}\mathrm{Js}.534.{10}^{14}\mathrm{Hz} \\ \mathrm{E}=3.54.{10}^{-19}\mathrm{J}/\mathrm{photons} \\ \mathrm{E}=3.54.{10}^{-19}\mathrm{J}.6.022.{10}^{23}{\mathrm{mol}}^{-1} \\ \mathrm{E}=213075\mathrm{J}/\mathrm{mol} \end{gathered}$$