Question

Which photons are most responsible for heating up a silicon photovoltaic panel in full sun: blue photons or infrared photons (beyond \(1.1 \mu \mathrm{m}\) )?

Short answer

Answer: Infrared photons (beyond \(1.1 \mu \mathrm{m}\)) are most responsible for heating up a silicon photovoltaic panel in full sun.

Step-by-step solution

Understand the given wavelengths and their corresponding energies.

The problem mentions blue photons (visible light) and infrared photons (beyond \(1.1 \mu \mathrm{m}\)). The energy of a photon can be calculated using the equation: \(E = \dfrac{hc}{\lambda}\), where E is the energy, h is Planck's constant (\(6.626 × 10^{-34} \ J\cdot s\)), c is the speed of light (\(2.998 × 10^8 \ m/s\)), and \(\lambda\) is the wavelength of the photon. Blue photons fall in the wavelength range of roughly 450-495 nm, or \(4.5 \times 10^{-7} \ m\) to \(4.95 \times 10^{-7} \ m\). Infrared photons beyond \(1.1 \mu \mathrm{m}\) have wavelengths larger than \(1.1 \times 10^{-6} \ m\).

Calculate the energy range of blue and infrared photons.

Using the given wavelength ranges, we can determine the energy ranges for both blue and infrared photons using the energy equation E = hc/λ. For blue photons: \(E_\text{blue} = \dfrac{(6.626 × 10^{-34} \ J\cdot s)(2.998 × 10^8 \ m/s)}{4.5 \times 10^{-7} \ m} \text{ to } \dfrac{(6.626 × 10^{-34} \ J\cdot s)(2.998 × 10^8 \ m/s)}{4.95 \times 10^{-7} \ m}\) For infrared photons beyond \(1.1 \mu \mathrm{m}\): \(E_\text{infrared} \leq \dfrac{(6.626 × 10^{-34} \ J\cdot s)(2.998 × 10^8 \ m/s)}{1.1 \times 10^{-6} \ m}\)

Compare the energies of blue and infrared photons.

We can see that blue photons have higher energies than infrared photons as their wavelengths are smaller. When these photons strike the silicon photovoltaic panel, they will transfer their energies to the electrons in the silicon material of the panel.

Determine the heating effect on the photovoltaic panel.

The silicon photovoltaic panel can only absorb photons with energies above its bandgap energy, which is approximately 1.1 eV. Blue photons have sufficient energy to excite electrons and contribute to the panel's electricity production. However, lower energy infrared photons will not be able to excite electrons across the bandgap but will still transfer their energy to the panel's material, causing a heating effect.

Conclusion:

Infrared photons (beyond \(1.1 \mu \mathrm{m}\)) are most responsible for heating up a silicon photovoltaic panel in full sun. This is because they have lower energies than blue photons and their energy is not sufficient to contribute to electricity production but still contributes to the heating effect on the panel.

Key concepts

Wavelength

The concept of wavelength is central to understanding electromagnetic radiation, including light, which consists of photons. Wavelength, denoted by the Greek letter \( \lambda \), is the distance between successive peaks of a wave and is typically measured in meters. The energy of a photon is inversely related to its wavelength through the equation: \[ E = \dfrac{hc}{\lambda} \]where \( E \) is energy, \( h \) is Planck's constant, and \( c \) is the speed of light.
Shorter wavelengths correspond to higher energy photons, such as those found in the blue end of the visible light spectrum, ranging from about 450-495 nm. Conversely, longer wavelengths, such as those beyond 1100 nm, represent lower energy photons, typically in the infrared range.
Understanding wavelength is crucial to differentiating between the energy profile of photons, such as distinguishing the high-energy blue photons from the lower-energy infrared photons.

Photovoltaic Panel

Photovoltaic panels, commonly known as solar panels, convert light into electricity using the photovoltaic effect. These panels are primarily made of semiconductor materials, most commonly silicon, that have properties enabling electron movement when energized by sunlight.
The energy a solar panel can harvest depends on photon energy. Blue photons, having higher energy due to their shorter wavelength, are effective in exciting electrons in the silicon, allowing them to cross the bandgap and contribute to electrical current.
For a photovoltaic panel to work efficiently:

• It needs photons with energy greater than its bandgap energy, around 1.1 eV for silicon.
• Photons with insufficient energy (like some infrared photons) will not contribute to electricity generation but may still heat the panel.

Understanding how different wavelengths affect solar panel performance is key to maximizing electricity production and managing heat dissipation.

Infrared Radiation

Infrared radiation lies beyond the red end of the visible spectrum and includes wavelengths longer than those visible to the human eye. Infrared photons have lower energy compared to visible light photons because of their longer wavelength, often being absorbed as heat rather than being used for electricity generation.
Infrared radiation can impact photovoltaic panels:

• Though these photons can't efficiently produce electricity due to their lower energy, they still transfer heat.
• This results in a rise in the temperature of the solar panel, affecting its efficiency.
• Understanding and managing this thermal effect is crucial for improving solar panel performance.

Infrared radiation's influence on solar technology showcases the intricate balance between capturing solar energy and managing thermal loads to keep the panels efficient and durable.