Answer:
a) n = 8 10⁴ , b) The energy of the electron is 9.6 10⁻¹⁹ J
Explanation:
The movement of the electron will approximate the movement within a potential pit with infinite walls, in this case the energy is given by
[tex]E_{n}[/tex] = (h² / 8mL) n²
Where n is an integer (n = 1, 2, 3 ...)
Let's reduce the distance to the SI system
L = 1 nm = 1 10⁻⁹ m
E = 6 eV (1.6 10⁻¹⁹J / 1 eV) = 9.6 10⁻¹⁹ J
Let's clear the equation
n = √ [(8m L / h²) E]
Let's calculate
n = √ [8 9.1 10⁻³¹ 1 10⁺⁹ /(6.63 10⁻³⁴)² 9.6 10⁻¹⁹]
n = √ (60,126 10⁸)
n = 7.8 10⁴
n = 8 10⁴
The energy of the electron is 9.6 10⁻¹⁹ J
