it\'s now almost possible (using integrated-circuit technology) to manufacture a

Question

it's now almost possible (using integrated-circuit technology) to manufacture a "box" that traps electrons in a region only a few nanometers wide.

Imagine we make an essentially one-dimensional box with a length of 3.0 nm. If we put 10 electrons in such a box and allow them to settle into the lowest energy states they can, consistent with Pauli exclusion principle, what will be the value of n for the highest energy level occupied? What will be the total energy of the electrons (ignoring their electrostatic repulsion)? Would your answer be different if the electrons were bosons instead of fermions?

Explanation / Answer

Given hat length of the one dimensional box is L = 3.0 *10^-9 m The value for the highest energy level is occupied is n = 5 Total energy of the electrons is E = n^2 h^2 / 8 m L^2                     = 5^2 (6.625*10^-34 J s )^2 / 8 ( 9.11*10^-31 kg) ( 3.0*10^-9 m)^2                    = 1.67*10^-19 J                                        = 1.67 eV

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