ATM-01

Rydberg formula

Hydrogen series lines.

Reading speed

AtomicRydberg

Governing equation

1/\lambda=R(1/n_1^2-1/n_2^2)

$n_2 \in \left[2, 12\right]$

where

n_1: n1 (—)
n_2: n2 (—)
\lambda: Wavelength (nm)

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.

00:0 / 00:08

①

Governing law — red

1/\lambda=R(1/n_1^2-1/n_2^2)

$n_2 \in \left[2, 12\right]$

$n_2 = 2$ $\lambda = 0$

Along the curve

②

Domain of the variable — blue

n_2_{\min} = 2,\quad n_2_{\max} = 12

$n_2 \in \left[2, 12\right]$

$n_2 = 2$ $n_2 = 2$

Along the curve

③

Response curve — green

1/\lambda=R(1/n_1^2-1/n_2^2)

$n_2 \in \left[2, 12\right]$

$n_2 = 2$ $\lambda = 0$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\lambda}{\mathrm{d}n_2}

$n_2 \in \left[2, 12\right]$

$n_2 = 2.063$ $\lambda^{\prime} = 25233.2$

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-01 — Rydberg formula) is the form associated with Rydberg. Working symbols: $n_1$ , $n_2$ $\rightarrow$ $\lambda$ . Hydrogen series lines.

Purpose

Purpose: compute

\lambda

from

n_1

n_2

in Atomic physics via

1/\lambda=R(1/n_1^2-1/n_2^2)

Hydrogen series lines. 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 = 2.000\,\mathrm{—}

n_2 = 4.000\,\mathrm{—}

, the governing relation

1/\lambda=R(1/n_1^2-1/n_2^2)

yields

\lambda = 486.01\,\mathrm{nm}

. Hydrogen series lines. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

n1 n_12 —n2 n_24 —

Outputs

Wavelength \lambda486.01 nm

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

Hydrogen series lines.

Reading speed

Watch on YouTube