Question

For the p-network of b-carotene modeled with the particle in the box approach, the position-dependent probability density of finding 1 of the 22 electrons is given by:

a) Schrödinger's equation
b) Heisenberg's uncertainty principle
c) Planck's constant
d) Hubble's law

Answer 1

The correct answer to the question about the probability density of an electron in β-carotene modeled with the particle in a box approach is the Heisenberg uncertainty principle.

Step-by-step explanation:

The question relates to the probability density of an electron in a β-carotene molecule, which is best described by the Heisenberg uncertainty principle. According to this principle, the more precisely the position of an electron is determined, the less precisely its momentum can be known, and vice versa. This is mathematically expressed by the equation ∆x∆p ≥ ħ/4π, where ∆x is the uncertainty in position, ∆p is the uncertainty in momentum, and ħ is the reduced Planck's constant. Furthermore, in quantum mechanics, the probability density function of finding an electron at a specific location is given by the square of the wavefunction, Ψ², which provides a distribution of probabilities in space. Therefore, the correct answer to the question is the Heisenberg uncertainty principle.