Determine the Energy of a Photon with a Given Wavelength

How can we calculate the energy of a photon with a wavelength of 334 nm?

What is the formula to determine the energy of a photon?

What are the values of Planck's constant and the speed of light in this calculation?

Calculating the Energy of a Photon

To determine the energy of a photon with a given wavelength of 334 nm, we can use the formula E = hf, where E represents the energy of the photon, h is Planck's constant (6.626 x 10^-34 J • s), and f is the frequency of the light.

Planck's constant and the speed of light are crucial in this calculation. Planck's constant is 6.626 x 10^-34 J • s, while the speed of light is 3.00 x 10^8 m/s.

Explanation of the Calculation

Firstly, we need to convert the given wavelength to frequency using the equation c = λf, where c represents the speed of light (3.00 x 10^8 m/s) and λ is the wavelength.

By rearranging the equation, we get f = c/λ. Substituting the given values into the equation, we find f = (3.00 x 10^8 m/s) / (334 nm * (1 m/10^9 nm)), which simplifies to f = 8.98 x 10^14 Hz.

Now, we can calculate the energy using the formula E = hf. Plugging in the values of Planck's constant and the frequency we calculated earlier, we get E = (6.626 x 10^-34 J • s) * (8.98 x 10^14 Hz), resulting in E = 5.95 x 10^-19 J.