Question

The blue color of the sky results from the scattering of sunlight by air molecules. The blue light has a frequency of about 7.5 x 1014 Hz. (a) Calculate the wavelength, in nm, associated with this radiation, and (b) calculate the energy, in joules, of a single photon associated with this frequency.

Answer 1

The wavelength associated with blue light of frequency 7.5 x 10^14 Hz is 400 nm, and the energy of a single photon at this frequency is 4.970 x 10^-19 Joules.

Step-by-step explanation:

To answer the student's question, we need to calculate (a) the wavelength in nanometers (nm) and (b) the energy in joules (J) of a single photon with a frequency of 7.5 x 1014 Hz.

(a) Calculate the Wavelength in nm

The speed of light, c, is a constant value of 3.00 x 108 meters per second (m/s), and the relationship between speed (c), frequency (f), and wavelength (λ) is given by c = f λ. We can rearrange this equation to solve for the wavelength (λ) as follows: λ = c / f.

Substituting the values, we get: λ = (3.00 x 108 m/s) / (7.5 x 1014 Hz) = 4.00 x 10-7 meters, which can be converted into nanometers: 400 nm (since 1 meter = 1 x 109 nm).

(b) Calculate the Energy in Joules

To find the energy of a single photon, we use the equation E = hf, where h is Planck's constant (6.626 x 10-34 J⋅s) and f is the frequency of the light. Substituting the given frequency into the equation yields: E = (6.626 x 10-34 J⋅s) (7.5 x 1014 Hz), which equates to: 4.970 x 10-19 J.