Question

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

Short answer

On a per-photon basis, ultraviolet radiation would yield more electrical energy than infrared radiation when converted using photovoltaic cells, assuming equal efficiency of conversion. This is because ultraviolet radiation has a higher frequency and therefore higher photon energy compared to infrared radiation as per the formula \(E=hf\).

Step-by-step solution

Understanding the energy of photons

The energy of a photon can be calculated using the formula: \( E = hf \) where \(E\) is the energy of the photon, \(h\) is the Planck's constant (6.63 × 10^-34 Js), and \(f\) is the frequency of the radiation.

Comparing the frequency of infrared and ultraviolet radiation

Infrared radiation has a lower frequency and longer wavelength than ultraviolet radiation. This can be confirmed by comparing their positions in the electromagnetic spectrum. In the spectrum, the order is as follows: Radio waves -> Microwaves -> Infrared -> Visible light -> Ultraviolet -> X-rays -> Gamma rays As we move from left to right in the spectrum, the frequency increases and wavelength decreases.

Calculating energy of infrared and ultraviolet photons

Due to the lower frequency of infrared radiation compared to ultraviolet radiation, a single photon of infrared radiation will have lower energy than a single photon of ultraviolet radiation. Using the formula mentioned in Step 1, we can conclude that: \(E_{UV} = hf_{UV}\) \(E_{IR} = hf_{IR}\) Since, \(f_{UV} > f_{IR}\), it follows that \(E_{UV} > E_{IR}\).

Conclusion

On a per-photon basis, ultraviolet radiation would yield more electrical energy than infrared radiation when converted using photovoltaic cells, assuming equal efficiency of conversion.

Key concepts

Photovoltaic Cells

Photovoltaic cells are devices that convert light into electrical energy. They play a crucial role in harnessing solar power. Made from semiconductor materials, typically silicon, these cells utilize the energy from photons to generate electricity.
When a photon hits the cell, its energy is transferred to an electron in the semiconductor. This energy causes the electron to break free from its usual position, creating an electron-hole pair. The material's electric field directs these free electrons, creating a flow of electric current when the cell is connected to an external circuit.
Photovoltaic cells operate efficiently across different parts of the electromagnetic spectrum; however, they typically perform better with higher-energy photons like those from ultraviolet light. This is because higher energy photons can stimulate more electrons than lower-energy ones like infrared.

Electromagnetic Spectrum

The electromagnetic spectrum is a range of all types of electromagnetic radiation. These radiations include:

• Radio waves
• Microwaves
• Infrared
• Visible light
• Ultraviolet
• X-rays
• Gamma rays

Each type of radiation in the spectrum has different wavelengths and frequencies.
As we move from radio waves to gamma rays on the spectrum, the frequency increases, and the wavelength decreases. This means ultraviolet light, which is further towards the gamma-ray side compared to infrared, has a higher frequency and hence higher energy per photon.
Understanding the electromagnetic spectrum helps us compare the energy potentials of different types of radiation when used in technologies like photovoltaic cells.

Ultraviolet Radiation

Ultraviolet (UV) radiation is part of the electromagnetic spectrum with higher frequencies than visible light but lower than X-rays. It is divided into three bands:

• UVA
• UVB
• UVC

These bands can penetrate the earth's atmosphere to varying degrees.
UV radiation has enough energy to cause chemical reactions and physical damage to materials, including biological tissues. Thus, it’s often associated with skin damage but also has beneficial uses, like sterilization.
In the context of photovoltaic cells, UV radiation, with its high-energy photons, can potentially generate more electricity than lower-energy infrared radiation. This makes UV an interesting candidate for maximizing electric output from solar cells.

Infrared Radiation

Infrared (IR) radiation is a part of the electromagnetic spectrum. It lies between the visible light and microwave regions. IR is noteworthy for its ability to transfer heat. It's often experienced as warmth from the sun, fires, or heaters.
Infrared light has lower energy per photon than visible or ultraviolet light, which means it produces less electric current per photon in photovoltaic cells.
However, it is abundant and can be used in various applications such as remote controls, thermal imaging, and night-vision technology. While it doesn't match the energy potential of UV radiation in photovoltaic conversion per photon, its ubiquity still makes it useful in certain applications.

Planck's Constant

Planck's constant (\(h\)) is a fundamental constant in physics, crucial to quantum mechanics. Its value is \(6.63 \times 10^{-34} \text{ Js}\). It relates the energy of a photon to its frequency by the formula:\[E = hf\]
This formula shows how energy increases with frequency: when frequency \(f\) is higher, energy \(E\) is greater, assuming \(h\) is constant.
Planck's constant is pivotal in explaining why ultraviolet radiation has more energy per photon than infrared radiation. This concept helps in the evaluation of different radiations for their potential to generate electrical power through devices like photovoltaic cells.