Problem 42 - Chemistry The Science in Context

Question

With reference to Problem \(7.41,\) could tungsten \((\phi=7.20 \times\) \(\left.10^{-19} \mathrm{J}\right)\) be used to construct solar cells?

Step-by-Step Solution

Answer

Answer: No, tungsten would not be an effective choice for constructing solar cells due to its high work function and the frequency of light required to excite electrons in tungsten being outside the visible light spectrum.

Step 1: Calculate the frequency of light required to excite electrons in tungsten

We are given the work function \(\phi=7.20 \times 10^{-19} \mathrm{J}\) and we know Planck's constant, \(h=6.63 \times 10^{-34} \mathrm{J\cdot s}\). We will now use the relation \(E = h\nu\) to find the frequency of light required to excite electrons in tungsten. Rearranging the equation for frequency, we get \(\nu = \frac{E}{h}\). By replacing the known values of \(E\) (work function) and \(h\) (Planck's constant), we get: \(\nu = \frac{7.20 \times 10^{-19} \mathrm{J}}{6.63 \times 10^{-34} \mathrm{J\cdot s}} = 1.09 \times 10^{15} \mathrm{Hz}\)

Step 2: Determine if the required frequency of light is within the visible light spectrum

The visible light spectrum ranges from approximately \(4 \times 10^{14} \mathrm{Hz}\) (red light) to \(8 \times 10^{14} \mathrm{Hz}\) (violet light). As we can see, the frequency of light required to excite electrons in tungsten (\(1.09 \times 10^{15} \mathrm{Hz}\)) is higher than the visible light frequency range. This means that, in general, the energy of photons in the visible light spectrum is not sufficient to excite electrons in tungsten and generate a current. Additionally, solar cells are designed to convert sunlight into electricity, and solar radiation does not typically produce a significant amount of light beyond the visible spectrum and near-infrared range. Due to the high frequency of light required to excite electrons in tungsten, it is unlikely to be a suitable material for solar cell construction. Therefore, tungsten would not be an effective choice for constructing solar cells.

Key Concepts

Tungsten

Tungsten is a chemical element best known for its exceptional physical properties. Its high melting point and remarkable strength make it suitable for many industrial applications. However, when it comes to solar cells, these attributes are not quite what we are looking for. To understand why, we need to grasp some basic concepts about electron excitation and solar cell function. In a solar cell, photons from sunlight strike the surface of the material, and their energy is absorbed to excite electrons, creating electricity. Tungsten, with its high work function, requires photons with very high energy to free these electrons. This makes it challenging to use for solar energy conversion, since ordinary sunlight does not typically contain enough high-energy photons.

Work Function

The work function of a material is the minimum energy needed to remove an electron from its surface. For tungsten, this energy requirement is quite high, at around \(7.20 \times 10^{-19} \mathrm{J}\). The work function is a crucial factor in solar cell design because it determines how easily electrons can be freed to create an electric current. A material with a lower work function can use lower energy photons to generate power. As a result, they can more efficiently make use of the broader sunlight spectrum, including the visible range. Tungsten's high work function means it needs higher frequency, higher energy photons that are less common in sunlight, making tungsten less effective for solar cell applications.

Visible Light Spectrum

The visible light spectrum is the portion of the electromagnetic spectrum that can be detected by the human eye. It ranges from red light, at about \(4 \times 10^{14} \mathrm{Hz}\), to violet light at around \(8 \times 10^{14} \mathrm{Hz}\). Solar cells are generally optimized to absorb light within this range because it represents the most abundant energy from the sun that reaches Earth. For materials used in solar cells, it's beneficial if the work function allows electron excitation using these frequencies. The required frequency to excite electrons in tungsten is \(1.09 \times 10^{15} \mathrm{Hz}\), which is above the visible spectrum. This means that standard sunlight which is primarily in the visible range cannot efficiently excite tungsten's electrons, making it impractical for use in solar cells.

Planck's Constant

Planck's constant, symbolized as \(h\), is a fundamental constant in physics that plays a vital role in quantum mechanics. Its value is \(6.63 \times 10^{-34} \mathrm{J\cdot s}\). This constant relates the energy of a photon to its frequency via the equation \(E = hu\). Understanding Planck's constant is crucial when calculating the frequency of light needed to excite electrons to overcome the work function of a material. For solar cells, a balance between the work function and the photon energy is essential to create a working system. If the work function is higher, as seen with tungsten, the corresponding light frequency, and thus photon energy, must also be high in order to excite electrons effectively. However, these higher energies are not typically found within the visible spectrum, which limits the effectiveness of tungsten in solar applications.