ATM-27

Bohr radius

Most-probable hydrogen radius.

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AtomicBohr radius

Governing equation

r_n=n^2 a_0/Z

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

where

n: n (—)
Z: Z (—)
r_n: Radius (pm)

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

r_n=n^2 a_0/Z

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

$n = 1$ $r_n = 52.92$

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

r_n=n^2 a_0/Z

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

$n = 1$ $r_n = 52.92$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}r_n}{\mathrm{d}n}

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

$n = 1.044$ $r_n^{\prime} = 110.5$

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-27 — Bohr radius) is the form associated with Bohr radius. Working symbols: $n$ , $Z$ $\rightarrow$ $r_n$ . Most-probable hydrogen radius.

Purpose

Purpose: compute

r_n

from

n

Z

in Atomic physics via

r_n=n^2 a_0/Z

Most-probable hydrogen radius. 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

n = 1.000\,\mathrm{—}

Z = 1.000\,\mathrm{—}

, the governing relation

r_n=n^2 a_0/Z

yields

r_n = 52.92\,\mathrm{pm}

. Most-probable hydrogen radius. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

n n1 —Z Z1 —

Outputs

Radius r_n52.92 pm

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Narration of this film

Most-probable hydrogen radius.

Reading speed

Watch on YouTube