Light relationships

Question

What is the wavelength in nanometers of photons with an energy of 69.0 ^kJ/_mol? in nm

Answer 1

Given

Energy of a photon = E = 69.0 kJ/mol

Asked for

wavelength = λ = ? nm

Calculations

E = hc / λ

E = energy of a photon = 69.0 kJ/mol = 69,000 J / mol

h = Planks constant = 6.626x10^-34 J-sec

c = speed of light = 3x10⁸ m/sec

λ = wavelength in m = ?

Solving for λ we have ... λ = hc/E

λ = (6.626x10^-34 J-sec)(3x10⁸ m/sec) / 69,000 J/mol

λ = 2.88x10^-30 m/mol

λ = (2.88x10^-30 m/mol)(1 mol / 6.02x10²³ photons) = 1.73x10^-6 m / photon

Converting to the requested units of nm, we have ...

1.73x10^-6 m / photon x 10⁹ nm / m = 1730 nm

(Be sure to check the math)