Calculate the energy of one photon of this slight check section 3–3 in astronomer toolbox 3–14 explanation use conversion one M equals 10^-9m traverse convert the nanometer to meter then plug numbers in the form

To calculate the energy of one photon, we can use the equation:

\[ E = \frac{hc}{\lambda} \]

Where:
- \( E \) is the energy of the photon,
- \( h \) is Planck's constant \((6.626 \times 10^{-34} \, \text{J}\cdot\text{s})\),
- \( c \) is the speed of light in a vacuum \((3.0 \times 10^8 \, \text{m/s})\),
- \( \lambda \) is the wavelength of the photon in meters.

### Steps:
1. **Convert the wavelength from nanometers to meters**: 
   \[
   \lambda (\text{m}) = \lambda (\text{nm}) \times 10^{-9}
   \]
   For example, if the wavelength is \( 500 \, \text{nm} \):
   \[
   \lambda (\text{m}) = 500 \times 10^{-9} \, \text{m} = 5.0 \times 10^{-7} \, \text{m}
   \]

2. **Plug the values into the equation**:
   \[
   E = \frac{(6.626 \times 10^{-34} \, \text{J}\cdot\text{s}) \times (3.0 \times 10^8 \, \text{m/s})}{5.0 \times 10^{-7} \, \text{m}}
   \]

3. **Calculate the energy**:
   \[
   E = \frac{1.9878 \times 10^{-25} \, \text{J}\cdot\text{m}}{5.0 \times 10^{-7} \, \text{m}} = 3.9756 \times 10^{-19} \, \text{J}
   \]

Thus, the energy of one photon with a wavelength of 500 nm is approximately \( 3.98 \times 10^{-19} \, \text{J} \).

Would you like a more detailed explanation or have any other questions?

Here are five related questions to expand your understanding:
1. What is the relationship between wavelength and photon energy?
2. How does the energy of a photon change with frequency?
3. How can you calculate the frequency of a photon given its wavelength?
4. What role does Planck’s constant play in quantum mechanics?
5. How do different wavelengths correspond to different types of electromagnetic radiation?

**Tip:** Always ensure the wavelength is converted to meters before plugging it into the photon energy formula for accurate results.

Learn how to calculate the energy of a photon by converting the wavelength from nanometers to meters and applying the equation E = hc/λ. This step-by-step solution covers key concepts in quantum mechanics and is suitable for students in Grades 11-12.

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