Problem 20 - Chemistry The Central Science

Question

It is possible to convert radiant energy into electrical energy using photovoltaic cells. Assuming equal efficiency of conversion, would infrared or ultraviolet radiation yield more electrical energy on a per-photon basis?

Step-by-Step Solution

Answer

On a per-photon basis, ultraviolet radiation would yield more electrical energy compared to infrared radiation, assuming equal efficiency of conversion in photovoltaic cells. This is because the energy of a photon is directly proportional to its frequency and the frequency of ultraviolet radiation is higher than that of infrared radiation.

Step 1: Understanding electromagnetic spectrum and radiant energy

The electromagnetic spectrum contains various types of waves, including infrared and ultraviolet radiation. Radiant energy is the energy carried by electromagnetic waves. The radiant energy carried by a wave is directly proportional to its frequency.

Step 2: Recall the energy of a photon formula

To determine the energy of a photon, we use the following formula: \(E = h\nu\) where \(E\) represents the energy of a photon, \(h\) is the Planck's constant (\(6.63 \times 10^{-34} Js\)), and \(\nu\) is the frequency of the electromagnetic wave.

Step 3: Understanding the position of infrared and ultraviolet radiation in the electromagnetic spectrum

In the electromagnetic spectrum, infrared radiation has a lower frequency compared to visible light, while ultraviolet radiation has a higher frequency compared to visible light. This means that the frequency of ultraviolet radiation is higher than the frequency of infrared radiation.

Step 4: Comparing the energy of infrared and ultraviolet photons

Since the energy of a photon is directly proportional to its frequency and the frequency of ultraviolet radiation is higher compared to infrared radiation, it follows that the energy per photon of ultraviolet radiation is greater than the energy per photon of infrared radiation.

Step 5: Conclusion

On a per-photon basis, ultraviolet radiation would yield more electrical energy compared to infrared radiation, assuming equal efficiency of conversion in photovoltaic cells.