Question

An electron that has an energy of approximately 6 eV moves between rigid walls with 1.00 nm of separation. Find: a. the quantum number n for the state of energy that the electron occupies. b. the precise energy of the electron.

Answer 1

a) n = 8 10⁴ , b) The energy of the electron is 9.6 10⁻¹⁹ J

Step-by-step 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

`E_(n)` = (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