# Answer to Question #197098 in General Chemistry for Moe

Question #197098

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

1
2021-05-25T07:50:16-0400

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 (NA = 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\u00d710^{-34}\\,J\\bcancel{s})(2.998\u00d710^{8}\\,\\bcancel{m}\/\\bcancel{s})(6.022\u00d710^{23}\\,mol^{-1})}{7\u00d710^{-7}\\,\\bcancel{m}}"

"E_{mole} =\\frac{(6.626)(2.998)(6.022)}{7}\u00d710^{-34+8+23+7} \\,J\\,mol^{-1}"

"E_{mole} =17.089\u00d710^{4} \\,J\\,mol^{-1} = 1.71\u00d710^{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.

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