The Physics Police

The Physics Police

Sunday, May 21, 2017

You contain more protons than neutrons

I just recently read this book The Greatest Story Ever Told by Lawrence Krauss. And I loved it! Normally I keep detailed book notes, especially on non-fiction books. This book was so interesting that I was paying close attention to its contents and neglected my notes. But I did write one thing down to research later on.

In chapter 10 Krauss says that neutrons
... make up most of the mass of heavier nuclei and thus most of the mass in our bodies.
This struck me as odd, because hydrogen has no neutrons and most of our body is made of water i.e. most of the atoms in our bodies are hydrogen. Sure, all other elements in our bodies have a ratio neutrons to protons is greater than one. But I wondered, which effect is larger? The extra neutrons from heavier, rarer elements, or the lack of neutrons from the most abundant element?

I won't keep you in suspense: he got it wrong. Protons win the popular vote for king of the nucleons. But it's a close race!

Element Abundance Z Average N N:Z Ratio Protons Neutrons
Oxygen 65.0% 8 8.00440 1.00055 5.200 5.202860
Carbon 18.5% 6 6.01100 1.00183 1.110 1.112035
Hydrogen 9.5% 1 0.00020 0.00020 0.095 0.000019
Nitrogen 3.2% 7 7.00400 1.00057 0.224 0.224128
Calcium 1.5% 20 20.11563 1.00578 0.300 0.301734
Phosphorus 1.0% 15 16.00000 1.06667 0.150 0.160000
Potassium 0.4% 19 20.13472 1.05972 0.076 0.080539
Sulfur 0.3% 16 16.09290 1.00581 0.048 0.048279
Sodium 0.2% 11 12.00000 1.09091 0.022 0.024000
Chlorine 0.2% 17 18.48000 1.08706 0.034 0.036960
Magnesium 0.1% 12 12.32000 1.02667 0.012 0.012320
Trace 0.1% 82 126.00000 1.53659 0.082 0.126000
Total 100%

7.353 7.328874

I started by finding the relative abundance by weight of different elements in the human body. Here you can see why the race is so close. Most of the atoms in your body are hydrogen but these atoms are so light that by weight they constitute less than 10% of your body mass.

Also, while every other element has an N:Z (neutron-to-proton) ratio greater than one, thy are all pretty darn close to one so the effect size is small. I was as generous as possible and assumed trace elements were all Lead-208, which has the highest N:Z ratio of stable isotope.

I think the moral of the story is to remember that nature can get complicated. We don't want to jump to a conclusion given one reasonable-sounding argument. Sometimes we have to work the problem all the way out to find the answer.

Or maybe Lawrence Krauss is prejudice against hydrogen?