Question

(a) How much energy (in kilojoules) is carried by one mole of photons of red light with$\lambda$= 650 nm?

(b) How many kilojoules are carried by one mole of photons of violet light with$\lambda$= 400 nm?

Short answer

The answers to the above questions are,

(a) E = 184 kJ/mol

(b) E = 299kJ/mol

Step-by-step solution

Calculate energy:

(a).We calculate energy using the equation:

E = h . v

$$\begin{gathered} \mathrm{E}=\mathrm{h}.\mathrm{v} \\ =\frac{\mathrm{h}.\mathrm{c}}{\mathrm{\lambda }} \\ =\frac{6.626.{10}^{-34}\mathrm{Js}.3.{10}^8\mathrm{m}/{\mathrm{s}}^2}{650.{10}^{-9}\mathrm{m}} \\ \mathrm{E}=3.06.{10}^{-19}\mathrm{J} \end{gathered}$$

In kJ/mol,

$$\begin{gathered} \mathrm{E}=3.06.{10}^{-19}{10}^{-3}\mathrm{J}.6.022.{10}^{23}{\mathrm{mol}}^{-1} \\ \mathrm{E}=184\mathrm{KJ}/\mathrm{mol} \end{gathered}$$

Calculate energyλ=400nm :

$$\begin{gathered} \mathrm{E}=\mathrm{h}.\mathrm{v} \\ =\frac{\mathrm{h}.\mathrm{c}}{\mathrm{\lambda }} \\ =\frac{6.626.{10}^{-34}\mathrm{Js}.3.{10}^8\mathrm{m}/{\mathrm{s}}^2}{650.{10}^{-9}\mathrm{m}} \\ \mathrm{E}=3.06.{10}^{-19}\mathrm{J} \\ \mathrm{in}\mathrm{KJ}/\mathrm{mol}, \\ \mathrm{E}=4.97.{10}^{-19}.{10}^{-3}\mathrm{J}.6.022.{10}^{23}{\mathrm{mol}}^{-1} \\ \mathrm{E}=299\mathrm{KJ}/\mathrm{mol} \end{gathered}$$