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

Given 4 ml of 0.13 M naphthalene solution.

Now find moles of naphthalene=Molarity xvolume=0.13 mol/Lx0.004 L

Moles of naphthalene=0.00052 mol.

We know that 1 mol=6.023x10^23 molecules.

So 0.00052 mol=6.023x10^23x0.00052 molecules

=3.13x10^20 molecules.

Now find the energy with wavelength=349 nm=349x10^-9 m.

From planks equation E=hc/wavelength

Where h=Planks constant=6.623x10^-34 Js,

c=velocity of light=3x10^8 m/s.

Therefore E=(6.623x10^-34 Jsx3x10^8 m/s)/349x10^-9 m

E=0.0569 x10^-17 J=5.69x10^-19 J/photon.

This is energy for single photon. Given naphthalene emits 12.8J energy.

Now find how many photons for 12.8 J energy=12.8 J/(5.69x10^-19 J/photon)=2.249x10^19 photons.

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

% emitted=(2.249x10^19/3.13x10^20 )×100

% emitted=71.83 %.