INGENIA
Index/Quantum mechanics/QNT-09

QNT-09

Hydrogen energy levels

En = −13.6 Z² / n² eV.

Reading speed
HydrogenBohr / Schrödinger

Governing equation

En=−13.6 eV Z2n2E_n=-13.6\,\mathrm{eV}\,\dfrac{Z^2}{n^2}

where

n
n (—)
Z
Z (—)
E_n
Energy (eV)

Lecture brief

Historical brief

Planck (1900), Einstein’s photoelectric law, Bohr, de Broglie, Heisenberg and Schrödinger’s 1926 equation rebuilt matter as amplitude. These sheets are the first solvable models: wells, spin, tunneling, uncertainty. This sheet (QNT-09 — Hydrogen energy levels) is the form associated with Bohr / Schrödinger. Working symbols: nn, ZZ →\rightarrow EnE_n. The Coulomb problem in QM reproduces Bohr's energies −13.6 Z²/n² eV, with degeneracy n² in the non-relativistic theory.

Purpose

Purpose: compute EnE_n from nn, ZZ in Quantum mechanics via En=−13.6 eV Z2n2E_n=-13.6\,\mathrm{eV}\,\dfrac{Z^2}{n^2} En = −13.6 Z² / n² eV. Use it when a real quantum mechanics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given n=1.000 —n = 1.000\,\mathrm{—}, Z=1.000 —Z = 1.000\,\mathrm{—}, the governing relation En=−13.6 eV Z2n2E_n=-13.6\,\mathrm{eV}\,\dfrac{Z^2}{n^2} yields En=−13.6000 eVE_n = -13.6000\,\mathrm{eV}. Hydrogen-like, infinite nuclear mass. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Outputs

  • Energy E_n-13.6000 eV
Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

QNT-09 · quantum
00:0 / 00:08

Narration of this film

Hydrogen-like, infinite nuclear mass.

The Coulomb problem in QM reproduces Bohr's energies −13.6 Z²/n² eV, with degeneracy n² in the non-relativistic theory.

Reading speed

Watch on YouTube