Question

A 6.00 mL ampule of a 0.120 M solution of naphthalene in hexane is excited with a flash of light. The naphthalene emits 18.3 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 = 18.3/5.696*10^-19

= 3.213*10^19

This is number of photons emitted

Number of mol of napthalene = M * V

=0.120 M * 6.00*10^-3 L

= 7.2*10^-4 mol

number of napthalene molecule = Number of mol * Avogadro’s number

= 7.2*10^-4 * 6.022*10^23

= 4.34*10^20 molecules

so,

% of particle emitted photon = number of photon * 100 / number of molecules

= (3.213*10^19)*100/(4.34*10^20)

= 7.41 %

Answer: 7.41 %