Question

What is the energy in joules of one mole of photons associated with red light of

wavelength 7.00 x 10² nm?

A. 1.71 x 105

J B. 12.4 kJ

C. 4.72 x 10^-43 J

D. 256 kJ

E. 2.12 x 10⁴² J

Answer 1

To calculate this energy per mole of photons we use the equation that relates the Planck's constant (h = 6.626 X 10^-34 Js), the velocity of light (c = 2.998 X 10⁸ m/s) , and wavelength [in meters] (λ = 7 X 10^-7 m) as:

$E_{photon}=\frac{h\cdot c}{\lambda}$

That was the energy per photon and we multiply it with Avogadro's constant (N_A = 6.022 * 10²³ mol^-1) to have the energy per mole:

$E_{mole} =N_A*E_{photon}=N_A\cdot\frac{h\cdot c}{\lambda}$

Substituting all the constants and wavelength give us as result:

$E_{mole} =\frac{(6.626×10^{-34}\,J\bcancel{s})(2.998×10^{8}\,\bcancel{m}/\bcancel{s})(6.022×10^{23}\,mol^{-1})}{7×10^{-7}\,\bcancel{m}}$

$E_{mole} =\frac{(6.626)(2.998)(6.022)}{7}×10^{-34+8+23+7} \,J\,mol^{-1}$

$E_{mole} =17.089×10^{4} \,J\,mol^{-1} = 1.71×10^{5} \,J\,mol^{-1}$

In conclusion, option A (1.71 X 10⁵ J) is the correct one.

Reference:

• Castellan, G. W. (1983). Physical Chemistry. Ed.