ATM-11

Hydrogenic ionisation

I = 13.6 Z² / n² eV. Energy to strip the last electron from level n.

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SpectraIonisation

Governing equation

I=13.6\,Z^2/n^2\,\mathrm{eV}

$Z \in \left[1, 26\right]$

where

Z: Atomic number (—)
n: Level n (—)
I: Ionisation 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

I=13.6\,Z^2/n^2\,\mathrm{eV}

$Z \in \left[1, 26\right]$

$Z = 1$ $I = 13.61$

Along the curve

②

Domain of the variable — blue

Z_{\min} = 1,\quad Z_{\max} = 26

$Z \in \left[1, 26\right]$

$Z = 1$ $Z = 1$

Along the curve

③

Response curve — green

I=13.6\,Z^2/n^2\,\mathrm{eV}

$Z \in \left[1, 26\right]$

$Z = 1$ $I = 13.61$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}I}{\mathrm{d}Z}

$Z \in \left[1, 26\right]$

$Z = 1.157$ $I^{\prime} = 31.49$

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-11 — Hydrogenic ionisation) is the form associated with Ionisation. Working symbols: $Z$ , $n$ $\rightarrow$ $I$ . He⁺ ground state is 54.4 eV. Inner-shell ionisation of heavy atoms is keV–MeV.

Purpose

Purpose: compute

I

from

Z

n

in Atomic physics via

I=13.6\,Z^2/n^2\,\mathrm{eV}

I = 13.6 Z² / n² eV. Energy to strip the last electron from level n. 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 = 2.000\,\mathrm{—}

n = 1.000\,\mathrm{—}

, the governing relation

I=13.6\,Z^2/n^2\,\mathrm{eV}

yields

I = 54.423\,\mathrm{eV}

. A bound electron, a continuum edge. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Atomic number Z2 —Level n n1 —

Outputs

Ionisation energy I54.423 eV

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Narration of this film

A bound electron, a continuum edge.

He⁺ ground state is 54.4 eV. Inner-shell ionisation of heavy atoms is keV–MeV.

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