Question

Electron transport chains (ETCs), large proteins through which electrons move, play important roles in two of nature's fundamental processes: (1) the conversion of electromagnetic energy from the Sun into the energy in the chemical bonds in glucose molecules and (2) the conversion of the energy in these glucose molecules into useful forms for metabolic processes, such as muscle contraction, building proteins, and respiration.
Respiratory ETCs are located in the inner membranes of mitochondria, the power plants of eukaryotic cells. ETCs have molecular mass of 800,000 atomic mass units (u), are about 20 nm long, and vary in width from 3 to 6 nm. Each ETC has sites at which an energetic "free" electron traveling through the chain can make temporary stops. Most of the resting sites have metal ions at their centers. At three places along the chain the electron-protein system goes into a significantly lower energy state ( ≈ 0.4 eV). The released energy catalyzes a reaction that converts two other molecules into ATP, which carries the energy gained to other parts of the cell for different processes that require chemical energy.
How does a lone energetic electron traverse such a long distance along the bumpy electrical potential hills and valleys of a large protein and not have its energy transformed into thermal energy or light? The answer is still uncertain but several possibilities have been proposed: (1) the ground state electron wave functions at resting sites are spread out (delocalized) over neighboring bonded atoms, which in turn are spread over and overlap with the next resting site; (2) an electron-atom system is excited into a higher energy, very delocalized state, after which the electron comes back down from this conduction state into a new location; or (3) the electron tunnels through the potential energy barrier between the resting sites. We'll examine briefly possibilities (2) and (3).
Explanation (2): Consider the visible spectra of metal atoms at the resting sites. If the excited state is delocalized over many atoms, as occurs in a semiconductor, this excited so-called conduction band is much broader than the excited state of a single atom. Thus, the visible spectra of a metal ion with a spread out excited conduction band should be somewhat broader than the excited state of a localized resting site with no conduction band. However, the observed visible spectra of the metal ion resting sites in ETCs look similar to metal ion sites found in other proteins not involved in electron conduction, with no apparent broader energy conduction band. Another problem with this explanation is the difficulty of exciting an electron at one site into the higher energy conduction band. The random kinetic energy at room temperature is about 0.025 eV, whereas visible spectra indicate that higher energy bands are 2-3 eV above the ground state. At room temperature, it is almost impossible to "promote" the electron to the conduction band.
Explanation (3): Tunneling can occur between the ground state of the atom at one site and an energy state at a nearby site--a state that is empty and slightly above the ground state. After the electron transfer, the electron-local atom system at the new site moves down to the slightly lower energy ground state, which prevents the electron from tunneling back. The system can also transition into a somewhat lower energy state and catalyze a reaction that converts the site's extra energy into the stable bond of some other molecule. Tunneling times seem consistent with measured electron transfer rates. But the actual transfer mechanism is still an open question.

1)Suppose that an ETC has 19 resting sites. If all of the electron resting sites were in a line along the length of an ETC, what would be the approximate distance from one site to the next?

2)Suppose the barrier height above the electron energy (Ubarrier−Eelectron) is 1.0 eV and the barrier is 2.0 nm wide. According to the uncertainty principle, what is the minimum time interval that the electron's energy is in this classically forbidden region?

3) The conduction band model of electron transport in electron transport chains may not work because...(Check all that apply)

the conduction band is too localized.

the electron has little chance of being "promoted" into the conduction band.

the visible spectrum of the resting site is not a broad band as is expected.

the electron transport chain is not entirely metal ions.

Answer 1

Question 3.

The conduction band model of electron transport in electron transport chains may not work because of the following reasons.

(i) The visible spectrum of the resting site is not broadband as is expected.

(ii) The electron transport chain is not entirely metal ions.