Question

A 4.00 mL ampule of a 0.130 M solution of naphthalene in hexane is excited with a flash of light. The naphthalene emits 12.8 J of energy at an average wavelength of 349 nm. What percentage of the naphthalene molecules emitted a photon?

Answer 1

we have:

wavelength = 3.49*10^-7 m

1st calculate energy of 1 photon

we have:

wavelength = 3.49*10^-7 m

we have below equation to be used:

Energy = Planck constant*speed of light/wavelength

=(6.626*10^-34 J.s)*(3.0*10^8 m/s)/(3.49*10^-7 m)

= 5.696*10^-19 J

number of photon = total energy/energy of 1 photon

n = 14.8/5.696*10^-19

= 2.598*10^19

number of mol of Napthalene = M*V

= 0.130 M * 4.00 mL

= 0.52 mmol

= 5.2*10^-4 mol

we have below equation to be used:

number of molecules = number of mol * Avogadro’s number

number of molecules = 5.2*10^-4 * 6.022*10^23 molecules

number of molecules = 3.13*10^20 molecules

% of molecules emitted = number of photons * 100 / number of molecules

= (2.598*10^19)*100/(3.13*10^20)

= 8.30 %

Answer: 8.30 %