A 2.00 mL ampule of a 0.110 M solution of naphthalene in hexane. The naphthalene emits 18.6 J of energy at an average wavelength of 349 nm.?

Let y% be the percentage of naphthalene molecules that emitted photons.

No. of moles of naphthalene molecules = (0.110 mol/L) × (2.00/1000 L) = 2.20 × 10⁻⁴ mol

Planck constant, h = 6.626 × 10⁻³⁴ J s
Speed of light, c = 3.00 × 10⁸ m/s
Wavelength of light, λ = 349 nm = 349 × 10⁻⁹ m
Avogadro constant, L = 6.022 × 10²³ /mol

Energy emitted in J :
(2.20 × 10⁻⁴) × y% × (Lhc/λ) = 18.6
y% = 18.6λ / [(2.20 × 10⁻⁴) × Lhc]
y = 1860λ / [(2.20 × 10⁻⁴) × Lhc]
y = 1860 × (349 × 10⁻⁹) / [(2.20 × 10⁻⁴) × (6.022 × 10²³) × (6.626 × 10⁻³⁴) × (3.00 × 10⁸)]
y = 24.6 (to 3 sig. fig.)

Hence, 24.6% of naphthalene molecules emitted photons.

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