Mole of naphthalene solution = 0.150
Molecules of naphthalene in the solution = 0.150 mol x (6.022 x 10²² molecules/1 mol) = 9.033 x 10²² molecules
Energy of a photon,
E = hγ = h. c/λ
where h is Planck's constant (6.626 x 10⁻³⁴) and γ is the frequency of light, c is the speed of light (3 x 10⁸) and is the λ wavelength of light.
Given, wavelength of light = 349 nm = 349 x 10⁻⁹ m ( 1 nm = 10⁻⁹ m)
Energy of one photon is,
E = 6.626 x 10⁻³⁴Js x (3 x 10⁸ms⁻¹ / 349 x 10⁻⁹ m)
E = 5.7 x 10⁻¹⁹ J
Energy emitted by naphthalene = 19.9 J
Therefore, the number of photons emitted = 19.9 J / 5.7 x 10⁻¹⁹ J = 3.5 x 10¹⁹
Percentage of naphthalene molecules that emitted a photon is
(photons emitted / total number of naphthalene) x 100
(3.5 x 10¹⁹/ 9.033 x 10²²) x 100
0.0387%
Thus 0.0387% naphthalene molecules emitted a photon.
