
determine the wavelength (nm) and energy (kJ/mol) for light with a frequency of 5.875 x 10^14 s^-1

To determine the **wavelength** and **energy** of light given its frequency, we can use the following key formulas:

### 1. Wavelength Calculation
The relationship between the frequency \(\nu\) and wavelength \(\lambda\) of light is given by the equation:
\[
\lambda = \frac{c}{\nu}
\]
Where:
- \(\lambda\) is the wavelength in meters (m),
- \(c = 3.00 \times 10^8 \, \text{m/s}\) is the speed of light,
- \(\nu = 5.875 \times 10^{14} \, \text{s}^{-1}\) is the frequency.

### 2. Energy Calculation
The energy \(E\) of a photon is related to its frequency by:
\[
E = h \nu
\]
Where:
- \(E\) is the energy of a single photon (in joules),
- \(h = 6.626 \times 10^{-34} \, \text{J·s}\) is Planck's constant,
- \(\nu = 5.875 \times 10^{14} \, \text{s}^{-1}\) is the frequency.

To find the energy in **kJ/mol**, we must first calculate the energy per photon and then multiply it by Avogadro's number, \(N_A = 6.022 \times 10^{23} \, \text{mol}^{-1}\).

Let's compute the results.The results are as follows:

1. **Wavelength**: \(510.64 \, \text{nm}\)
2. **Energy**: \(234.42 \, \text{kJ/mol}\)

Would you like more details or have any questions? Here are 5 related questions to deepen your understanding:

1. How does wavelength relate to the color of light?
2. What is the energy of a single photon at this frequency in joules?
3. How do wavelength and frequency affect energy?
4. What is the relationship between the speed of light, frequency, and wavelength?
5. How would changing the frequency affect the energy of light?

**Tip**: Wavelength in nanometers often helps to identify the type of electromagnetic radiation (e.g., visible light, UV, infrared).

determine the wavelength (nm) and energy (kJ/mol) for light with a frequency of 5.875 x 10^14 s^-1

Learn how to calculate the wavelength (510.64 nm) and energy (234.42 kJ/mol) for light with a frequency of 5.875 x 10^14 s^-1 using the speed of light and Planck's constant. This problem demonstrates key principles of wave-particle duality, including the relationship between frequency, wavelength, and energy. Suitable for high school and college students.

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