Question #197098

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

wavelength 7.00 x 10^{2} 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 10^{42} J

Expert's answer

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 10^{8} 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 * 10^{23} 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 10**^{5}** J) is the correct one. **

Reference:

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

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