ATM-25

Balmer formula

1/λ = R (1/4 − 1/n²), n = 3,4,5,… Visible hydrogen from n=2.

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SpectraBalmer

Governing equation

\dfrac1\lambda=R_\infty\left(\dfrac14-\dfrac1{n^2}\right)

$n \in \left[3, 12\right]$

where

n: Upper n (—)
\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.

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①

Governing law — red

\dfrac1\lambda=R_\infty\left(\dfrac14-\dfrac1{n^2}\right)

$n \in \left[3, 12\right]$

$n = 3$ $\lambda = 656.1$

Along the curve

②

Domain of the variable — blue

n_{\min} = 3,\quad n_{\max} = 12

$n \in \left[3, 12\right]$

$n = 3$ $n = 3$

Along the curve

③

Response curve — green

\dfrac1\lambda=R_\infty\left(\dfrac14-\dfrac1{n^2}\right)

$n \in \left[3, 12\right]$

$n = 3$ $\lambda = 656.1$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\lambda}{\mathrm{d}n}

$n \in \left[3, 12\right]$

$n = 3.057$ $\lambda^{\prime} = -313.2$

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-25 — Balmer formula) is the form associated with Balmer. Working symbols: $n$ $\rightarrow$ $\lambda$ . Hα is n=3 → 2 at 656.3 nm. The series limit is 364.6 nm.

Purpose

Purpose: compute

\lambda

from

n

in Atomic physics via

\dfrac1\lambda=R_\infty\left(\dfrac14-\dfrac1{n^2}\right)

1/λ = R (1/4 − 1/n²), n = 3,4,5,… Visible hydrogen from n=2. 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 = 3.000\,\mathrm{—}

, the governing relation

\dfrac1\lambda=R_\infty\left(\dfrac14-\dfrac1{n^2}\right)

yields

\lambda = 656.11\,\mathrm{nm}

. A visible series, a red Hα. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Upper n n3 —

Outputs

Wavelength \lambda656.11 nm

Reading speed

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Narration of this film

A visible series, a red Hα.

Hα is n=3 → 2 at 656.3 nm. The series limit is 364.6 nm.

Reading speed

Watch on YouTube