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 the naphthalene molecules emitted a photon?

Verified step by step guidance

1. Calculate the number of moles of naphthalene in the solution using the formula: \( \text{moles} = \text{concentration} \times \text{volume} \).
2. Convert the volume from mL to L to ensure consistency in units.
3. Determine the total number of naphthalene molecules using Avogadro's number: \( \text{number of molecules} = \text{moles} \times 6.022 \times 10^{23} \).
4. Calculate the energy of a single photon using the formula: \( E = \frac{hc}{\lambda} \), where \( h \) is Planck's constant, \( c \) is the speed of light, and \( \lambda \) is the wavelength.
5. Determine the number of photons emitted by dividing the total energy emitted by the energy of a single photon, and then calculate the percentage of naphthalene molecules that emitted a photon by dividing the number of photons by the total number of naphthalene molecules and multiplying by 100.

Key Concepts

Photon Emission

Photon emission occurs when an excited electron in a molecule returns to a lower energy state, releasing energy in the form of a photon. The energy of the emitted photon can be calculated using the equation E = hc/λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is the wavelength. Understanding this process is crucial for determining how many molecules emitted photons based on the total energy released.

Molarity and Volume

Molarity (M) is a measure of concentration defined as the number of moles of solute per liter of solution. In this question, the naphthalene solution has a concentration of 0.100 M, and the volume is 5.00 mL. To find the total number of moles of naphthalene present, one must convert the volume from milliliters to liters and then apply the molarity formula, which is essential for calculating the number of molecules involved in the photon emission.

Percentage Calculation

Calculating the percentage of naphthalene molecules that emitted a photon involves determining the ratio of the number of molecules that emitted photons to the total number of naphthalene molecules present. This is expressed as a percentage by multiplying the ratio by 100. Understanding how to perform this calculation is key to answering the question accurately and interpreting the results in the context of molecular behavior.