Final answer:
The wavelength and frequency of light emitted from an electron moving from n=3 to n=1 in a hydrogen atom can be calculated using the Rydberg formula and the speed of light equation, resulting in a specific value for the wavelength and frequency which characterize the photon emitted during this transition.
Step-by-step explanation:
The student asks for the calculation of the wavelength and frequency of light emitted by a hydrogen atom when an electron transitions from the n=3 energy level to the n=1 energy level. According to the Rydberg formula for the hydrogen atom, the wavelength (λ) can be calculated using the formula: 1/λ = R(1/n²1 - 1/n²2), where R is the Rydberg constant (1.097 x 107 m-1), n1 is the lower energy level, and n2 is the higher energy level. Substituting n1 = 1 and n2 = 3, we get 1/λ = R(1/12 - 1/32), which yields the wavelength for this transition.
Once the wavelength is known, the frequency (ν) can be found using the speed of light equation c = λν, where c is the speed of light in a vacuum (3 x 108 m/s). By rearranging this formula, we find ν = c/λ. After plugging in the values for the speed of light and the calculated wavelength, we can determine the frequency of the emitted light.