Final answer:
To calculate the wavelength of light that contains 4.02 x 10^-19 J of energy, we use the equation λ = hc / E. After substituting the constants for Planck's constant and the speed of light, and performing the calculation, the wavelength is approximately 4.95 x 10^-7 meters, which is closest to option B.
Step-by-step explanation:
The question is asking to calculate the wavelength of light in meters that corresponds to a given amount of energy, which is 4.02 x 10-19 joules per photon. We need to use the equation that relates the energy of a photon to its wavelength, which is given by the Planck-Einstein relation:
E = hc / λ
Where:
- E is the energy of the photon in joules (J)
- h is Planck's constant (6.626 x 10-34 J⋅s)
- c is the speed of light in a vacuum (3.0 x 108 m/s)
- λ is the wavelength of the photon in meters (m)
To find the wavelength λ, we rearrange the formula:
λ = hc / E
Substitute the known values into the equation:
λ = (6.626 x 10-34 J⋅s ⋅ 3.0 x 108 m/s) / (4.02 x 10-19 J)
After performing the calculation, we find that λ is approximately 4.95 x 10-7 meters, which is not exactly matching any of the given options. However, it's closest to option B) 7.48 x 10-7 meters.