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7.00ml ampule of a 0.150 mole solution naphthalene in hexane is excited with a flash of light. The naphthalene emits 19.9J of energy at an average wavelength of 349 NMMI. What percentage of naphthalene molecules emitted a photon?
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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.

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