Calculating the Energy of a Photon

What is the energy of a photon with a wavelength of 617 nm?

The energy of the photon with a wavelength of 617 nm can be calculated using the formula:

E = hc/λ

Where:

E is the energy of the photon

h is Planck's constant (approximately 6.626 x 10^-34 J·s)

c is the speed of light (approximately 3.00 x 10^8 m/s)

λ is the wavelength of the photon

Step 1: Convert the wavelength from nanometers (nm) to meters (m):

617 nm = 617 x 10^-9 m

Step 2: Substitute the values into the equation:

E = (6.626 x 10^-34 J·s) x (3.00 x 10^8 m/s) / (617 x 10^-9 m)

Step 3: Calculate the energy of the photon:

E ≈ 3.21 x 10^-19 J

Understanding the Calculation

When calculating the energy of a photon, the formula E = hc/λ is used, where h is Planck's constant and c is the speed of light. The key step in the calculation is to convert the wavelength from nanometers to meters to ensure consistent units.

Step 1: The wavelength of 617 nm is converted to meters by multiplying by 10^-9 to get 617 x 10^-9 m.

Step 2: The values for h, c, and the converted wavelength are substituted into the equation E = hc/λ.

Step 3: The energy of the photon is calculated as approximately 3.21 x 10^-19 J, with the correct number of significant digits.

By following these steps and using the appropriate constants, we can accurately determine the energy of a photon based on its wavelength.