Problem 42 - Chemistry: An Atoms-Focused Approach

Question

With reference to Problem \(3.41,\) could tin \((\Phi=6.20 \times\) \(\left.10^{-19} \mathrm{J}\right)\) be used to construct solar cells?

Step-by-Step Solution

Answer

Answer: No, tin is not suitable for constructing solar cells based on absorbing visible radiation, as its work function (6.20 x 10^-19 J) is higher than the energy of the most energetic photons in the visible region (4.97 x 10^-19 J). Using tin as the material for solar cells might result in poor efficiency and low power generation.

Step 1: Understand the concept of work function and solar cells

The work function (Φ) of a material is the minimum amount of energy required to remove an electron from the surface of that material. In the context of solar cells, this energy corresponds to the energy required to create electron-hole pairs, which are responsible for the flow of electrical current. For a material to be suitable for solar cell construction, it should be capable of absorbing and converting enough solar energy to produce a significant amount of electron-hole pairs, thus generating electrical current.

Step 2: Determine the energy of solar radiation

To determine if tin is suitable for solar cell construction, we need to compare its work function to the energy obtained from sunlight. The solar radiation at Earth's surface has an energy range including ultraviolet (UV), visible, and infrared (IR) regions. The most energetic photons in the visible region have a wavelength of around 400 nm. We can calculate the energy of these photons using the Planck's equation: E = (h × c) / λ, where E is energy, h is Planck's constant (6.626 x 10^-34 Js), c is the speed of light (3 x 10^8 m/s), and λ is the photon's wavelength.

Step 3: Calculate the energy of the most energetic photons in the visible region

Using the constants and given wavelength: E = (6.626 x 10^-34 Js * 3 x 10^8 m/s) / (400 x 10^-9 m) E ≈ 4.97 x 10^-19 J

Step 4: Comparing work function of tin with solar radiation energy

Now we compare the work function of tin (Φ = 6.20 x 10^-19 J) with the energy of the most energetic photons in the visible region (E ≈ 4.97 x 10^-19 J). Since the work function of tin is higher than the energy of most visible photons, tin would not be suitable for constructing solar cells that are primarily based on absorbing visible radiation for generating electron-hole pairs. Using tin as the material for solar cells might result in poor efficiency and low power generation.

Key Concepts

Work Function

The term "work function" refers to the minimum amount of energy required to remove an electron from the surface of a material. This energy is crucial in determining how effectively a material can participate in photovoltaic processes.
For a material to be practical in solar cell applications, it must possess a work function compatible with the energy of incoming solar photons. Too high a work function compared to the photon energy means that electrons won't be easily released, inhibiting electricity generation.

• Solar cells made from materials with a suitable work function can efficiently convert sunlight into electrical energy by releasing electrons.
• If the work function is higher than the photon energy, fewer electrons will be released, leading to reduced efficiency.

This makes choosing the right material critical for solar technology innovation.

Electron-Hole Pairs

In solar cells, electricity is generated primarily through the creation of electron-hole pairs. When a photon strikes a material, its energy can excite an electron, freeing it from its bound state and creating an electron-hole pair.
Electrons, once freed, leave behind holes. These pairs are crucial because:

• They form the charge carriers that move through the solar cell, enabling an electric current to flow.
• The number of electron-hole pairs generated directly impacts the solar cell's power output.
• Materials need a work function that allows effective creation of these pairs from available photon energies.

Therefore, understanding how electron-hole pairs form is key to enhancing solar cell efficiency.

Solar Radiation Energy

Solar energy that reaches Earth is composed of a spectrum of electromagnetic radiation. This spectrum includes ultraviolet (UV), visible, and infrared (IR) light.
The energy available from the sun is vital because it dictates the types of materials suitable for solar cells. For example:

• The visible spectrum is most crucial for solar cells, as it carries a significant portion of the solar power received on Earth.
• The energy of sunlight must be converted effectively to electrical energy within the cell to be practical.
• Comparing a material's work function with the solar radiation energy helps in assessing its suitability for use in solar cells.

Thus, understanding solar radiation energy enables us to better design materials that can efficiently harness solar power.

Visible Photon Energy

Photons in the visible spectrum are particularly important when considering solar cell material choices. The most energetic of these photons have a wavelength around 400 nm.
Using Planck's equation, we can calculate the energy of photons in the visible range. These energies are typically compared with work functions to determine if a material can liberate electrons effectively.

• Materials need to have a work function lower than or comparable to the energy from visible photons to be efficient.
• The calculated energy for the most energetic visible photons is approximately 4.97 x 10^-19 J.
• If this energy is lower than the material’s work function, such as with tin, it's not considered ideal for solar cells relying primarily on visible light.

Knowing visible photon energy aids in the evaluation of potential solar cell materials.