Question

What is implied about the energy requirements of photosystems I and II by the fact that there is a difference in the minimum wavelength of light needed for them to operate \((700 \mathrm{nm} \text { for photosystem } \mathrm{I} \text { and } 680 \mathrm{nm}\) for photosystem II )

Short answer

Photosystem II has higher energy requirements than Photosystem I because it requires light with a shorter wavelength and thus higher energy.

Step-by-step solution

Understand the Concept of Wavelength and Energy

The energy of light is inversely proportional to its wavelength. This means that the shorter the wavelength, the higher the energy of the light. This relationship is given by the equation: \[ E = \frac{hc}{\lambda} \] where \(E\) is the energy, \(h\) is Planck's constant, \(c\) is the speed of light, and \(\lambda\) is the wavelength.

Compare Wavelengths of Photosystems I and II

Photosystem I operates at a minimum wavelength of 700 nm, while Photosystem II operates at a minimum wavelength of 680 nm. Since 680 nm is shorter than 700 nm, the light required for Photosystem II has higher energy than that for Photosystem I.

Relate Wavelength to Energy Requirements

Given the inverse relationship between wavelength and light energy, Photosystem II requires light with higher energy compared to Photosystem I. This implies that Photosystem II has higher energy requirements than Photosystem I to operate.

Key concepts

Wavelength and Energy Relationship

The relationship between wavelength and energy is crucial for understanding photosystems. Light energy is inversely proportional to its wavelength. This means that as the wavelength of light decreases, the amount of energy increases and vice versa. This relationship is described by the equation: \[ E = \frac{hc}{\lambda} \]where:

• \(E \) is the energy of the photon,
• \(h\) is Planck's constant \((6.626 \times 10^{-34} \text{J} \cdot\text{s})\),
• \(c\) is the speed of light \((3 \times 10^8\text{m} / \text{s})\), and
• \(\lambda\) is the wavelength of light.

Given this equation, if a photon has a shorter wavelength, it will have higher energy. Conversely, a longer wavelength means less energy.

Photosystem I

Photosystem I (PSI) is one of the two photosystems in the photosynthetic light reactions. It is primarily involved in capturing light energy and converting it into chemical energy. PSI gets activated by light with a wavelength of 700 nm. This wavelength is comparatively longer and thus the energy associated with it is lower.
PSI plays a key role in producing NADPH, a crucial molecule for the Calvin cycle. Because PSI operates at a longer wavelength, the energy requirement is lower compared to Photosystem II.

Photosystem II

Photosystem II (PSII) is the first protein complex in the light-dependent reactions of oxygenic photosynthesis. It captures photons and uses the energy to extract electrons from water molecules, releasing oxygen as a by-product. PSII operates at a minimum wavelength of 680 nm, which is shorter than the wavelength required by PSI, indicating that it requires higher energy light.
This higher energy requirement means that PSII has to absorb light of higher energy to drive its reactions. Hence, PSII initiates the light reactions with higher energy photons, setting off the electron transport chain.

Planck's Constant

Planck's constant is a fundamental constant in quantum mechanics denoted by \(h\). Its value is approximately \(6.626 \times 10^{-34} J \cdot s\). Planck's constant is key in determining the energy of photons.
Through Planck's equation \[ E = \frac{hc}{\lambda} \] we can see that it relates the energy of a photon (\(E\)) to its frequency (or inversely to its wavelength \(\lambda\)). Planck's constant establishes that energy quantization is a fundamental feature of light and all electromagnetic radiation.

Speed of Light

The speed of light, denoted by \(c\), is a constant value used in many scientific equations. Its value is \(3 \times 10^8 \text{m}/\text{s}\). This constant is critical when calculating energy because it appears in the equation:
\[ E = \frac{hc}{\lambda} \]where the speed of light is multiplied by Planck's constant and divided by the wavelength of the light. This demonstrates that the speed of light, along with Planck's constant, helps determine the energy carried by a photon. This is essential in understanding the different energy requirements of Photosystem I and II.