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ATM-32

Reduced mass

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Atomicreduced mass

Governing equation

μ=mM/(m+M)\mu=mM/(m+M)

M∈[0.1,250]M \in \left[0.1, 250\right]

where

m
Light (u)
M
Heavy (u)
\mu
Reduced (u)

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①

Governing law — red

μ=mM/(m+M)\mu=mM/(m+M)

M∈[0.1,250]M \in \left[0.1, 250\right]

M=0.1M = 0.1μ=5.45×10−4\mu = 5.45\times 10^{-4}

②

Domain of the variable — blue

Mmin⁡=0.1,Mmax⁡=250M_{\min} = 0.1,\quad M_{\max} = 250

M∈[0.1,250]M \in \left[0.1, 250\right]

M=0.1M = 0.1M=0.1M = 0.1

③

Response curve — green

μ=mM/(m+M)\mu=mM/(m+M)

M∈[0.1,250]M \in \left[0.1, 250\right]

M=0.1M = 0.1μ=5.45×10−4\mu = 5.45\times 10^{-4}

④

Rate of change — amber

dμdM\frac{\mathrm{d}\mu}{\mathrm{d}M}

M∈[0.1,250]M \in \left[0.1, 250\right]

M=1.672M = 1.672μ′=9.21×10−7\mu^{\prime} = 9.21\times 10^{-7}

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-32 — Reduced mass) is the form associated with reduced mass. Working symbols: mm, MM →\rightarrow μ\mu. Nucleus recoils.

Purpose

Purpose: compute μ\mu from mm, MM in Atomic physics via μ=mM/(m+M)\mu=mM/(m+M) Nucleus recoils. 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=5.480e−4 um = 5.480e-4\,\mathrm{u}, M=1.007 uM = 1.007\,\mathrm{u}, the governing relation μ=mM/(m+M)\mu=mM/(m+M) yields μ=5.477e−4 u\mu = 5.477e-4\,\mathrm{u}. Nucleus recoils. Move a slider: the numbers are this situation, not a canned story.

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Inputs

Outputs

  • Reduced \mu0.000548 u
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Narration of this film

Nucleus recoils.

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