ATM-10

Reduced-mass Rydberg

μ = m M / (m+M), R_μ = R_∞ μ / m_e. Finite-mass shift of the spectrum.

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StructureReduced mass

Governing equation

\mu=mM/(m+M),\quad R_\mu=R_\infty\mu/m_e

where

M: Nuclear mass (u)
\mu/m_e: Reduced mass (—)
R_\mu: Rydberg (1/m)

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-10 — Reduced-mass Rydberg) is the form associated with Reduced mass. Working symbols: $M$ $\rightarrow$ $\mu/m_e$ , $R_\mu$ . Hydrogen versus deuterium: the Balmer lines shift by about 0.17 nm. Positronium has μ = m/2.

Purpose

Purpose: compute

\mu/m_e

R_\mu

from

M

in Atomic physics via

\mu=mM/(m+M),\quad R_\mu=R_\infty\mu/m_e

μ = m M / (m+M), R_μ = R_∞ μ / m_e. Finite-mass shift of the spectrum. 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

M = 1.008\,\mathrm{u}

, the governing relation

\mu=mM/(m+M),\quad R_\mu=R_\infty\mu/m_e

yields

\mu/m_e = 0.999456\,\mathrm{—}

R_\mu = 1.1e+7\,\mathrm{1/m}

. Two masses, a reduced μ, a slightly smaller R. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Nuclear mass M1.0078 u

Outputs

Reduced mass \mu/m_e0.999456 —
Rydberg R_\mu10967761.4 1/m

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Narration of this film

Two masses, a reduced μ, a slightly smaller R.

Hydrogen versus deuterium: the Balmer lines shift by about 0.17 nm. Positronium has μ = m/2.

Reading speed

Watch on YouTube