Here is an interesting query that I put to Gemini:
What percentage of matter in the universe is made of protons and neutrons. In what proportion are these two particles.
Here was the response:
Protons and neutrons—collectively known as baryonic matter—make up 4.9% of the total mass-energy of the universe, or 15.6% of all matter when excluding dark energy. Within that baryonic pool, protons outnumber neutrons by a ratio of roughly 7 to 1 (about 87.5% protons to 12.5% neutrons by particle count).
1. Percentage of Matter in the Universe
Because cosmology distinguishes between the total mass-energy budget (\(E = mc^2\)) and the matter-only budget, there are three ways to express how much of the universe consists of protons and neutrons (based on Planck satellite measurements of the Cosmic Microwave Background):
| Cosmic Reference Frame | Percentage Made of Protons & Neutrons | What Else Is Included? |
|---|---|---|
| Total Mass-Energy of the Universe | ~4.9% (\(\Omega_b \approx 0.049\)) | Dark Energy (~68.5%) and Dark Matter (~26.6%) dominate the cosmic budget. |
| All Gravitationally Clustering Matter | ~15.6% (\(\frac{\Omega_b}{\Omega_m} = \frac{4.9\%}{31.5\%}\)) | Dark Matter (~84.4%) accounts for the remaining five-sixths of all matter. |
| Ordinary (Visible/Atomic) Matter | ~99.95% (by mass) | Electrons (~0.05%) and trace neutrinos. Since a proton is \(1,836\times\) more massive than an electron, nucleons carry virtually all atomic mass. |
2. Proportion of Protons to Neutrons (~7:1)
The 7:1 proton-to-neutron ratio was locked in during the first three minutes after the Big Bang (Big Bang Nucleosynthesis) and has only shifted slightly over the 13.8 billion years since.
Step 1: The Thermal "Freeze-Out" (~1 Second After the Big Bang)
In the first fraction of a second, the universe was hot enough (\(T > 10^{10}\text{ K}\)) for protons (\(p\)) and neutrons (\(n\)) to rapidly interconvert via weak nuclear interactions:
$$n + \nu_e \leftrightarrow p + e^- \quad \text{and} \quad n + e^+ \leftrightarrow p + \bar{\nu}_e$$Because a neutron (\(939.565\text{ MeV}/c^2\)) is slightly heavier than a proton (\(938.272\text{ MeV}/c^2\)) by a mass difference of \(\Delta m = 1.293\text{ MeV}/c^2\), converting a proton into a neutron requires a small energy input. As the universe expanded and cooled to the "freeze-out" temperature (\(k_B T \approx 0.8\text{ MeV}\)) at roughly \(t \approx 1\text{ second}\), the weak interaction rate dropped below the expansion rate of the universe. At that moment, the ratio froze according to the Boltzmann factor:
$$\frac{n}{p} = e^{-\Delta m / k_B T} \approx e^{-1.293 / 0.8} \approx \frac{1}{6}$$At one second old, there were 6 protons for every 1 neutron.
Step 2: Free Neutron Decay (~1 to 180 Seconds)
Before neutrons could fuse with protons into stable helium nuclei, the universe had to cool enough that high-energy photons stopped blasting newly formed deuterons (\(^2\text{H}\)) apart (the "deuterium bottleneck"). During this ~3-minute waiting period, free neutrons—which are unstable outside a nucleus with a mean lifetime of \(\tau_n \approx 878\text{ seconds}\) (a half-life of ~10.2 minutes)—underwent beta decay into protons:
$$n \rightarrow p + e^- + \bar{\nu}_e$$By the time nucleosynthesis ignited in earnest around \(t \approx 180\text{ seconds}\), beta decay had eroded the ratio from 6:1 to 7:1 (87.5% protons, 12.5% neutrons).
Step 3: Locking Neutrons into Helium-4
Once the temperature dropped below \(10^9\text{ K}\), nearly every surviving neutron was swept up into Helium-4 (\(^4\text{He}\)) nuclei (each containing 2 protons and 2 neutrons), which has an exceptionally high binding energy per nucleon.
To see how a 7:1 particle ratio produces the famous 75% Hydrogen / 25% Helium mass split of the universe, consider a group of 16 nucleons (14 protons and 2 neutrons):
- The 2 neutrons pair with 2 protons to form 1 Helium-4 nucleus (mass = 4 units).
- The remaining 12 protons stay alone as 12 Hydrogen-1 nuclei (mass = 12 units).
- By mass: \(\frac{12}{16} = \mathbf{75\%\text{ Hydrogen}}\) and \(\frac{4}{16} = \mathbf{25\%\text{ Helium-4}}\).
- By nucleon count: \(\frac{14}{16} = \mathbf{87.5\%\text{ protons}}\) and \(\frac{2}{16} = \mathbf{12.5\%\text{ neutrons}}\) (7:1).
Step 4: Stellar Fusion Over 13.8 Billion Years (~6.7:1 Today)
Over cosmic history, stars have fused primordial hydrogen into more helium and heavier elements (carbon, oxygen, iron), converting a small fraction of protons into neutrons via the proton-proton chain and supernovae. Because the vast majority of baryonic matter still resides in diffuse intergalactic gas clouds that have never cycled through a star, stellar fusion has only nudged the cosmic mass fraction from ~75% H / 25% He to roughly 73% Hydrogen, 25% Helium, and 2% heavier elements.
This shifts the modern cosmic ratio very slightly from 7.0 : 1 at the end of the Big Bang to roughly 6.7 : 1 today (~87% protons to ~13% neutrons).
Explore the cosmic mass-energy breakdown
Explore the cosmic mass-energy breakdown and step through how the proton-to-neutron ratio evolved from the first second of the Big Bang to the modern universe:
