SCIENCE · INVESTIGATE AND EXPLAIN

Close primordial baryon bookkeeping without claiming a full network

A hot expanding early universe permits nuclear reactions only during a changing interval of temperature and density. Light-element abundances therefore depend on expansion, reaction rates, baryon density and neutron survival. Helium, deuterium and other species provide different constraints; a single endpoint count is not a complete nucleosynthesis calculation.

Learning outcome: Count neutrons, protons, nuclei and baryons separately, then track unbound-neutron decay. Name a light-element or rate constraint missing from the endpoint model.

Starting recap

Keep galaxy mass, source calibration, expansion history and independent cosmological evidence distinct.

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Try

At r=0.15 and f=1, helium number is 0.075 and helium baryon amount 0.3. Total baryons are 1.15, so helium fraction is 0.3/1.15≈0.260870 and hydrogen fraction≈0.739130. This is a supplied endpoint example, not a quoted observed primordial abundance.

Open the experiment

Predict

Why does the number of helium nuclei differ from the baryon amount locked into helium?

Your prediction and reason

Experiment

Count neutrons, protons, nuclei and baryons separately, then track unbound-neutron decay. Name a light-element or rate constraint missing from the endpoint model.

Count baryons before interpreting an abundance

Worked teaching model · synthetic values · Original endpoint bookkeeping starts with proton amount 1 and neutron amount r. Fraction f of neutrons forms He 4; two neutrons and two protons per nucleus. Unbound neutrons later decay into protons, ignoring tiny mass defects in baryon mass fractions. Not a nuclear-reaction network or quantitative primordial abundance prediction.

Initial neutron/proton number ratio: 0.15 ratio Fraction of initial neutrons bound into helium 4: 1 fraction

Reset keeps your prediction, captures and practice history.

Endpoint baryon accounting is necessary but not a full prediction of primordial element abundances.

Original endpoint bookkeeping starts with proton amount 1 and neutron amount r. Fraction f of neutrons forms He 4; two neutrons and two protons per nucleus. Unbound neutrons later decay into protons, ignoring tiny mass defects in baryon mass fractions. Not a nuclear-reaction network or quantitative primordial abundance prediction.

Original conditional model ledger
Quantity	Value	Unit
Helium 4 nuclei	0.07500000	initial-proton number units
Protons remaining before neutron decay	0.8500000	number units
Unbound neutrons before decay	0	number units
Hydrogen nuclei after unbound neutron decay	0.8500000	number units
Helium baryon mass fraction	0.2608696	fraction
Hydrogen baryon mass fraction	0.7391304	fraction
Final total baryon count	1.150000	number units

These supplied models are not current measured cosmological parameters, a new galaxy discovery or independent actual observing evidence.

Endpoint baryon accounting is necessary but not a full prediction of primordial element abundances.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

1. Define the cosmic evidence

2. Connect mechanisms and alternatives

The original bookkeeping starts with proton number one and neutron number r. Fraction f of the initial neutrons is incorporated into helium-4. Each helium nucleus needs two neutrons and two protons, so helium number is fr/2 and it contains 2fr baryons. Remaining free protons are 1−fr and remaining neutrons r(1−f).

The unbound neutrons are then stipulated to decay into protons. Hydrogen number becomes 1−fr+r(1−f), while total baryon count remains 1+r. Ignoring the small binding/rest-mass differences for this count-based mass fraction, helium fraction is 2fr/(1+r) and hydrogen is the complement. Electrons and emitted neutrinos are not counted as baryons.

This endpoint model does not calculate when reactions freeze out, trace deuterium or lithium, or infer a measured baryon density. Expansion observations, background radiation and primordial abundance measurements probe different aspects of the hot-big-bang framework. Questions about the earliest boundary or the microscopic identity of dark matter remain distinct from evidence for an earlier hot dense state.

3. Work the supplied comparison

4. Predict and investigate

Why does the number of helium nuclei differ from the baryon amount locked into helium?

Count neutrons, protons, nuclei and baryons separately, then track unbound-neutron decay. Name a light-element or rate constraint missing from the endpoint model.

Apply the evidence to a changed case

Use r=0.1 and f=0.8. Find helium number, surviving free neutrons before decay and final helium baryon fraction.

Retain the evidence frame, calculations and assumptions before opening public feedback.

Compare a worked response

Helium number is 0.04, unbound neutrons 0.02 and helium baryon amount 0.16. Final hydrogen number is 0.92+0.02=0.94; total 1.10 gives helium fraction 0.16/1.10≈0.145455. Both endpoint fractions sum to one.

Source and boundaries

Primary source. Checked 31 October 2026. Original model records are not new galaxy observations, current parameter measurements or a full cosmological inference pipeline. No physical observing procedure is requested.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Use r=0.1 and f=0.8. Find helium number, surviving free neutrons before decay and final helium baryon fraction.

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

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Previous: Separate a cosmic angular scale from ruler calibration Next: Propagate a calibrated source through orbital and radiative inferences

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