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.