Question

A 1.00 mL ampule of a 0.150 M solution of naphthalene in hexane is excited with a flash of light. The naphthalene emits 12.5 J of energy at an average wavelength of 349 nm. What percentage of the naphthalene molecules emitted a photon?

Answer 1

First use the formula, E = hc/λ

(6.626 x 10^-34 Js x 3 x 10⁸ ms^-1)/ (349 x 10^-9 m) = 5.695 x 10^-19J

Number of the photons emitted = (12.5 J) / (5.695 x 10^-19J) photons

                                                   = 2.195 x 10^-19 photons

Moles of naphthalene = volume in (L) x molarity

                                   = (0.001 x 0.150) mole

                                   = (1.50 x 10^-4) mole

Number of its molecules = Moles / Avogrado number

                                      = (1.50 x 10^-4) x (6.023 x 10²³)

                                      = 9.035 x 10^-19 molecules

Percentage of the naphthalene molecules emitted a photon = (2.195 x 10^-19) / (9.035 x 10^-19) x 100

                                                                                                = 24.3%