Question

A 5.00 ml ampule of a 0.100 M solution of naphthalene in hexane is excited with a flash of light. The naphthalene emits 15.5 J of energy at an average wavelength of 349 nm. What percentage of naphthalene molecules emitted a photon?

Answer 1

Molarity of solution = 0.100 M

Volume of ampule = 5.00 mL

Moles of naphthalene = 0.100 * 0.005

= 0.0005

Molecules of naphthalene = 0.0005 * 6.023*10²³

= 3.011x10²⁰

Energy emitted = 15.5 J

Wavelength = 349 nm = 349x10^-9 m

Let the number of photons emitted be n.

Energy emitted = n*h*c /

15.5 = n * 6.626x10^-34 * 3x10⁸ / 349x10^-9

15.5 = n * 0.0569x10^-17

n = 2.72x10¹⁹  

Percentage of naphthalene molecules emitted a photon = (2.72x10¹⁹) / (3.011x10²⁰)

= 9.03 %