An ampule of naphthalene in hexane contains 5.00×10−4mol
 naphthalene. The naphthalene is excited with a flash of light and then emits 18.4 J
 of energy at an average wavelength of 349 nm
. What percentage of the naphthalene molecules emitted a photon?

To solve this problem, we need to determine what percentage of the naphthalene molecules emitted a photon when excited.

### Steps:

1. **Energy of a photon**:
   The energy of a single photon is given by the equation:
   
   \[
   E = \frac{hc}{\lambda}
   \]

   Where:
   - \( h = 6.626 \times 10^{-34} \, \text{J·s} \) is Planck's constant,
   - \( c = 3.00 \times 10^8 \, \text{m/s} \) is the speed of light,
   - \( \lambda = 349 \, \text{nm} = 349 \times 10^{-9} \, \text{m} \) is the wavelength of the emitted light.

2. **Calculate energy per photon**:
   Let's calculate the energy of a single photon using the given wavelength of 349 nm.

\[
E_{\text{photon}} = \frac{(6.626 \times 10^{-34}) \times (3.00 \times 10^8)}{349 \times 10^{-9}} \, \text{J}
\]

Let me calculate that.The energy of a single photon emitted at a wavelength of 349 nm is approximately \( 5.70 \times 10^{-19} \, \text{J} \).

3. **Total number of photons emitted**:
   To find the total number of photons emitted, divide the total emitted energy (18.4 J) by the energy of a single photon:

   \[
   N_{\text{photons}} = \frac{18.4 \, \text{J}}{5.70 \times 10^{-19} \, \text{J/photon}}
   \]

Let me calculate that.The total number of photons emitted is approximately \( 3.23 \times 10^{19} \).

4. **Total number of naphthalene molecules**:
   The number of naphthalene molecules is determined by multiplying the number of moles by Avogadro's number (\( N_A = 6.022 \times 10^{23} \)):

   \[
   N_{\text{molecules}} = 5.00 \times 10^{-4} \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol}
   \]

Let's calculate the number of naphthalene molecules.The total number of naphthalene molecules is approximately \( 3.01 \times 10^{20} \).

5. **Percentage of molecules that emitted a photon**:
   To find the percentage of naphthalene molecules that emitted a photon, we divide the number of photons emitted by the total number of naphthalene molecules and multiply by 100:

   \[
   \text{Percentage} = \left( \frac{N_{\text{photons}}}{N_{\text{molecules}}} \right) \times 100
   \]

Let me calculate that.It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like more details on the steps, or do you have any other questions? Here are five related questions to explore:

1. How is the energy of a photon related to its wavelength?
2. What are some practical applications of naphthalene's light emission properties?
3. How does the percentage of molecules that emit photons change with energy?
4. What is Planck's constant and why is it important in quantum mechanics?
5. How would using a different wavelength affect the photon emission calculations?

**Tip:** Always check units in calculations to ensure consistency and accuracy, especially in physics problems.

An ampule of naphthalene in hexane contains 5.00×10−4 mol naphthalene. The naphthalene is excited with a flash of light and then emits 18.4 J of energy at an average wavelength of 349 nm. What percentage of the naphthalene molecules emitted a photon?

Solve a physics problem involving the calculation of the percentage of naphthalene molecules that emitted photons when excited. This problem covers key concepts such as photon energy calculation, moles to molecules conversion, and percentage determination. Suitable for college-level physics students.

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