Question

A 5.00 mL ampule of a 0.110 M solution of naphthalene in hexane is excited with a flash of light. The naphthalene emits 12.1 J of energy at an average wavelength of 349 nm. What percentage of the naphthalene molecules emitted a photon?

Answer 1

first find the energy of a single photon associated with that given wavelength, then use the total energy emitted by the sample to figure out exactly how many photons were emitted.

now find moles of naphthalene C10H8 were present in the sample.

moles = 0.110 M x 0.005 L = 0.00055 moles

Finally, convert the moles of naphthalene to molecules and compare the number of photons with the number of molecules.

E = h.v

(E - the energy of the photon, ν - its frequency , h - Planck's constant, equal to 6.626x10⁻³⁴J s)

ν⋅λ = c

( λ - the wavelength of the photon, c - the speed of light in a vacuum, usually given as 3x10⁸m s⁻¹)

E = h⋅c / λ

E = 6.626x10⁻³⁴Js x 3x10⁸ms⁻¹ / 349x10^-9 m

E = 5.696 x 10⁻¹⁹J

If this is the energy of a single photon of wavelength 349 nm, it follows that the total energy of 12.1 J corresponds to

12.1J x (1 photon) / 5.696 x10⁻¹⁹J = 2.1243 x10¹⁹ photons

Now that you know how many photons were emitted, focus on finding how many molecules of naphthalene were present in solution.

one mole of any substance contains 6.022x10²³ molecules of that substance.

Use Avogadro's number as a conversion factor to help you find how many molecules of naphthalene you have in that many moles

0.00055 moles x 6.022x10²³molec / 1 mole = 3.3121 x10²⁰molecules

The percentage of the naphthalene molecules that emitted a photon will thus be equal to

% emitted = ( 2.1243x10¹⁹ / 3.3121x10²⁰) x100 % = 6.413 %