Final answer:
Using the energy of a photon formula and the given frequencies, we deduce that the microwave oven at 2.5 GHz generates more photons per second than the heat lamps at a combined frequency of 1.7×105 GHz, as it has a lower frequency and thus each photon has less energy.
Step-by-step explanation:
To determine which way generates more photons between the microwave oven at a frequency of 2.5 GHz and the heat lamps at a combined frequency of 1.7×105 GHz, we must first understand the relationship between the frequency of electromagnetic radiation and the energy of a single photon. The energy of a photon (E) is given by the equation E = hf, where h is Planck's constant (6.626×10-34 J·s) and f is the frequency of the radiation.
Given that both the microwave oven and the heat lamps output the same amount of energy per second (750 J), the system with the lower frequency (microwave oven) will generate more photons, as each photon has less energy compared to those from the higher frequency system (heat lamps).
To calculate, using the formula E = hf, let's find out the energy per photon for each:
- For the microwave oven: E = (6.626×10-34 J·s)(2.5×109 Hz) = 1.6565×10-24 J per photon
- For the heat lamps: E = (6.626×10-34 J·s)(1.7×105 GHz) = 1.12642×10-28 J per photon
Then, to find the number of photons generated per second, we divide the total energy output per second by the energy per photon:
- For the microwave oven: 750 J/s ÷ 1.6565×10-24 J = 4.527×1026 photons/s
- For the heat lamps: 750 J/s ÷ 1.12642×10-28 J = 6.655×1029 photons/s
Thus, the microwave oven at 2.5 GHz generates more photons than the heat lamps at 1.7×105 GHz when both output the same energy per second.