Question

An ultraviolet lamp emits light of wavelength 400 nm at the rate of 400 w. an infrared lamp emits light of wavelength 700 nm, also at the rate of 400 w.

(a) which lamp emits photons at the greater rate and (b) what is that greater rate?

Answer 1

The infrared lamp emits photons at a greater rate because each of its photons has less energy compared to those of the ultraviolet lamp due to the longer wavelength (700 nm versus 400 nm). Despite both lamps having the same power output, the lower energy per photon in the infrared lamp results in a higher emission rate of photons.

Step-by-step explanation:

The rate at which a lamp emits photons depends on both the power output of the lamp and the energy of the individual photons it emits. The energy of a photon is given by the equation E = hc/λ, where 'h' is Planck's constant, 'c' is the speed of light, and 'λ' is the wavelength of the light. Since the ultraviolet lamp emits light of shorter wavelength (400 nm) compared to the infrared lamp (700 nm), the energy of each ultraviolet photon is greater than that of each infrared photon.

Given that both lamps emit at the same power (400 W), the lamp emitting the lower energy photons (the infrared lamp) will emit a greater number of photons per second. To determine the actual rate, we would use the equation Power (P) = Energy per photon (E) × Number of photons per second (n), and solve for n, which would yield a higher photon emission rate for the infrared lamp due to its longer wavelength (700 nm).