Question

Electron transfer between redox centers in proteins is controlled by quantum tunneling. We can model the region between two redox centers as an energy barrier which the electron must cross. If the distance between the redox centers is 0.681 nm and the energy of the electron is 0.5540.554eV lower than the height of the barrier, what is the probability that the electron will successfully cross to the next redox center

Answer 1

5.61 e⁻³

Step-by-step explanation:

Given that:

The barrier length = 0.681 nm = 6.81 × 10⁻¹⁰

The difference between the height of the barrier & the energy of the electron is;

`V - E = 0.554 \ eV (1.6 * 10^(-19) )`

= 8.864 × 10⁻²⁰ V

where;

m = 9.1 × 10⁻³¹ kg

The probability
`P = e^(-2 \ kd)`

`k = 2 \pi \sqrt{(2m (V-E))/(h^2) }`

`k = 2 \pi * \frac{\sqrt{2 * 9.1 * 10^(-31) * 8.864 * 10^(-20)}}{6.63 * 10^(-34)}`

k = 3.806 × 10⁹

`P = e^(-2 \ kd)`

`P = e^{2 * 3.806 * 10^9 * 6.81 * 10^(-10)}`

P = 0.005606

P = 5.61 × 10⁻³

P = 5.61 e⁻³