Final answer:
To calculate the energy of a photon given its wavelength, use the equation E = hc/λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength.
Step-by-step explanation:
To solve for the energy of a photon when given the wavelength, we use the equation E = hf, where E is the energy, h is Planck's constant, and f is the frequency of the photon. Since frequency can be expressed in terms of wavelength through the equation c = λf, where c is the speed of light and λ is the wavelength, we can rewrite the energy equation as E = hc/λ. Here, h is Planck's constant (6.626 × 10-34 J × s), c is the speed of light (approximately 3 × 108 m/s), and λ is the wavelength of the photon in meters.
For example, to find the energy of a red photon with a wavelength of 630 nm (which is 630 × 10-9 meters), you would substitute these values into the equation:
E = (6.626 × 10-34 J × s)(3 × 108 m/s) / (630 × 10-9 m)
After calculating, you would obtain the energy in joules (J).