Question

Manybiologicalelectrontransferreactions,suchasthose associated with biological energy conversion, may be visualized as arising from electron tunneling between protein-bound cofactors, such as cytochromes, quinones, flavins, and chlorophylls. This tunneling occurs over distances that are often greater than 1.0 nm, with sections of protein separating electron donor from acceptor. For a specific combination of electron donor and acceptor, the rate of electron tunneling is proportional to the transmission probability, with k ≈ 7 nm−1 (eqn 9.11). By what factor does the rate of electron tunneling between two co-factors increase as the distance between them changes from 2.0 nm to 1.0 nm?

Answer 1

Answer:

The tunneling rate will increase by a million fold i.e by a factor of 1,000,000

Explanation:

The detailed steps is as shown by applying transmission probabilities and ratio of tunelling.

Answer 2

The rate of electron tunneling increases by a factor of about a million fold.

Given the following data:

• Distance 1 = 1.0 nm.

• Distance 2 = 2.0 nm.

• k = 7 nm.

The rate of tunneling and transmission probability.

In Quantum mechanics, the rate of tunneling is directly proportional to the transmission probability of an electron. Thus, a ratio of the rate of tunneling is equal to a ratio of the transmission probability that corresponds to it.

Mathematically, this ratio is given by this expression:

$\frac{T_1}{T_2} =\frac{1+\frac{(e^{kL_2}-e^{kL_2})^2}{16\epsilon(1-\epsilon)} }{1+\frac{(e^{kL_1}-e^{kL_1})^2}{16\epsilon(1-\epsilon)} }$

Note: This tunneling occurs over distances that are often greater than 1.0 nanometer.

Therefore, we have:

$\frac{(e^{kL_2}-e^{kL_2})^2}{16\epsilon(1-\epsilon)} > > 1$

Simplifying further, we have:

$\frac{T_1}{T_2} =\frac{e^{xL_2}-e^{xL_2})^2}{e^{xL_1}-e^{xL_1})^2} \\\\\frac{T_1}{T_2} =e^{2k(L_2-L_1)}\\\\\frac{T_1}{T_2} =e^{2\times 7\times10^{-9}(2-1)\times10^{-9}}\\\\\frac{T_1}{T_2} =e^{14}\\\\\frac{T_1}{T_2} =1.2 \times 10^6$

Therefore, the rate of electron tunneling increases by a factor of about a million fold.

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