Question

A 9.00 mL ampule of a 0.140 M solution of naphthalene in hexane is excited with a flash of light. The naphthalene emits 11.3 J of energy at an average wavelength of 349 nm. What percentage of the naphthalene molecules emitted a photon?

Answer 1

Given:

lambda = 3.49*10^-7 m

1st calculate energy of 1 photon

Given:

lambda = 3.49*10^-7 m

use:

E = h*c/lambda

=(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 = 11.3/5.696*10^-19

= 1.984*10^19

So, 1.984*10^19 molecules have emitted photon

Lets now calculate the total number of molecules available.

Use:

number of mol = Molarity * volume in L

= 0.140 M * 0.009 L

= 1.26*10^-3 mol

number of molecule present = number of mol * Avogadro’s number

= 1.26*10^-3 * 6.022*10^23

= 7.59*10^20

% of molecules emitting photons = number of molecules emitting photon * 100 / total number of molecule present

= (1.984*10^19)*100 / (7.59*10^20)

= 2.61 %

Answer: 2.61 %