QNT-21

Rydberg photon

Hydrogen series line.

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GoverningRydberg photon

Governing equation

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

$n2 \in \left[2, 12\right]$

where

n1: n1 (—)
n2: n2 (—)
lam: Rydberg photon (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.

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①

Governing law — red

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

$n2 \in \left[2, 12\right]$

$n2 = 2.063$ $lam = 6072.5$

Along the curve

②

Domain of the variable — blue

n2_{\min} = 2,\quad n2_{\max} = 12

$n2 \in \left[2, 12\right]$

$n2 = 2.063$ $n2 = 2.063$

Along the curve

③

Response curve — green

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

$n2 \in \left[2, 12\right]$

$n2 = 2.063$ $lam = 6072.5$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}lam}{\mathrm{d}n2}

$n2 \in \left[2, 12\right]$

$n2 = 2.126$ $lam^{\prime} = -30706$

Along the curve

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-21 — Rydberg photon) is the form associated with Rydberg photon. Working symbols: $n1$ , $n2$ $\rightarrow$ $lam$ . Hydrogen series line. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

lam

from

n1

n2

in Quantum mechanics via

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

Hydrogen series line. 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

n1 = 2.000\,\mathrm{—}

n2 = 4.000\,\mathrm{—}

, the governing relation

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

yields

lam = 486.174\,\mathrm{nm}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

n1 n12 —n2 n24 —

Outputs

Rydberg photon lam486.174 nm

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Hydrogen series line. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube