ATM-26

Bohr energy

Hydrogen-like levels.

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AtomicBohr

Governing equation

E_n=-13.6 Z^2/n^2~\mathrm{eV}

$n \in \left[1, 8\right]$

where

Z: Z (—)
n: n (—)
E_n: Energy (eV)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

E_n=-13.6 Z^2/n^2~\mathrm{eV}

$n \in \left[1, 8\right]$

$n = 1$ $E_n = -13.6$

Along the curve

②

Domain of the variable — blue

n_{\min} = 1,\quad n_{\max} = 8

$n \in \left[1, 8\right]$

$n = 1$ $n = 1$

Along the curve

③

Response curve — green

E_n=-13.6 Z^2/n^2~\mathrm{eV}

$n \in \left[1, 8\right]$

$n = 1$ $E_n = -13.6$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}E_n}{\mathrm{d}n}

$n \in \left[1, 8\right]$

$n = 1.044$ $E_n^{\prime} = 23.99$

Along the curve

Lecture brief

Historical brief

Balmer, Rydberg, Bohr (1913), fine structure, Zeeman and Stern–Gerlach built the spectrum of one atom. The lab computes levels, selection and magnetic splitting. This sheet (ATM-26 — Bohr energy) is the form associated with Bohr. Working symbols: $Z$ , $n$ $\rightarrow$ $E_n$ . Hydrogen-like levels.

Purpose

Purpose: compute

E_n

from

Z

n

in Atomic physics via

E_n=-13.6 Z^2/n^2~\mathrm{eV}

Hydrogen-like levels. Use it when a real atomic physics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

Z = 1.000\,\mathrm{—}

n = 1.000\,\mathrm{—}

, the governing relation

E_n=-13.6 Z^2/n^2~\mathrm{eV}

yields

E_n = -13.600\,\mathrm{eV}

. Hydrogen-like levels. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Z Z1 —n n1 —

Outputs

Energy E_n-13.600 eV

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Narration of this film

Hydrogen-like levels.

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