Determine the wavelength and frequency for light with energy of 252.4 kJ/mol

Answer 1

Yellow light has a frequency of 570 - 590 nm. Let us use 580 nm as an average.

E = hc / λ

E = energy = 252.5 kJ/mol

h = Planck's constant = 6.626x10^-34 J-sec

c = speed of lilght = 3x10⁸ m/sec

λ = frequency = 580 nm = 580x10^-9 m (changed to meters to match units of c)

Before solving we should convert the energy to a per photon, instead of per mol of photons

252.5 kJ /mol photons x 1 mol photons / 6.02x10²³ photons = 4.19x10^-22 kJ / photon

4.19x10^-22 kJ/photon x 1 J / 1x10^-3 kJ = 4.19x10^-19 J / photon

E = hc / λ

4.19x10^-22 kJ = (6.626x10^-34 Js) (3x10⁸ m/s) / λ

λ = 4.74x10^-4 J

(be sure to check all of the math)