The Radii and Densities of Elementary Particles and Periodic Table Nucleons

Dr. Ardeshir Irani

IntelliPaper

− Abstract

We calculate the size as the radius of a sphere, along with the density of all the elementary particles of the first column of the Standard Model of Particle Physics viz. the Up and Down quarks, the electron, the electron neutrino, the proton, the neutron, and the nuclei of all the elements and isotopes of the Periodic Table, using their known masses and the previously calculated radii (r) of the electron and the electron neutrino since re/re = me/me, can be extended further to calculate rp, rn, rUp, rDown and their densities, and rNucleon Number with a Table of nucleon radii that increase and nucleon density that decrease as the number of nucleons increase. The radii of the largest size nuclei can be observed experimentally by electron microscopes as confirmation of the theoretical calculations.

I. INTRODUCTION

We consider only the elementary particles of the first column of the Standard Model of Particle Physics because the elementary particles of the second and third columns are all unstable except for the three neutrinos of all three columns that are known to change flavor. The unstable elementary particles of the second and third columns decay into the elementary particles of the first column, and that is the reason the atoms that make up the four states of matter and the elements of the Periodic Table consist of protons, neutrons, and electrons as the building blocks of the Universe. We calculate for only stable nuclei and their isotopes, not considering unstable nuclei with exceptions made either because of their abundance, longevity or importance to calculate their radii and densities.

II. RADIUS CALCULATIONS

Starting with the radius of the electron = $4.68 \times 10^{-16}$ m (Reference 1) and the radius of the electron neutrino = 2x $10^{-21}$ m (Reference 2) and the mass of the electron = 0.511 MeV/ $c^{2}$ and the mass of the electron neutrino = 2.2 eV/ $c^{2}$ from the Standard Model of Particle Physics we see that the ratio of their radii is equal to the ratio of their masses. $r_{e}/r_{v_{e}} = m_{e}/m_{v_{e}} = 4.68 \times 10^{-16}/2 \times 10^{-21} = 0.511 \times 10^{6}/2.2 = 2.3 \times 10^{5}$ . We use this equality ratio of the radius and mass to calculate the radius of the proton, the neutron, the Up and Down Quarks, and the elements of the Periodic Table.

For the Neutron: $r_{n}/r_{e}=m_{n}/m_{e}$ , $r_{n}=(939.57/0.511)\times4.68\times10^{-16}=8.605\times10^{-13}\mathrm{~m}8.61\times10^{-13}\mathrm{~m}$ .

For the Up Quark: $r_{Up}/r_{e}=m_{Up}/m_{e}$ , $r_{Up}=(2.3/0.511)\times4.68\times10^{-16}=2.1\times10^{-15}\mathrm{~m}$ .

For the Down Quark: $r_{Down}/r_{e}=m_{Down}/m_{e}$ , $r_{Down}=(4.8/0.511)\times4.68\times10^{-16}=4.4\times10^{-15}\mathrm{~m}$ .

We change the unit of calculation from $MeV/c^{2}$ to atomic mass units (u) for convenience while calculating the sizes of the stable nuclei and their stable isotopes.

formula we use is $r_{X} = 8.52 \times 10^{-13} m_{X}$ and we use the Tables of Nuclear Data (Reference 3) to determine $m_{X}$ where x refers to the nucleon number and $m_{X}$ refers to the mass of that nucleus in amu (u) to calculate the radius $r_{X}$ of its nucleus in meters.

1. Hydrogen H $(r_{1,2})$ $m_{H1}\rightarrow 8.59\mathrm{x}10^{-13}\mathrm{m},m_{H2}\rightarrow 1.72\mathrm{x}10^{-12}\mathrm{m}.$

Implying $r_{H1} = 8.59 \times 10^{-13} \, m$ , $r_{H2} = 1.72 \times 10^{-12} \, m$ , and so on for all the remaining elements that have been calculated below:

Helium He $(r_{3,4})$ $m_{He3} \to 2.57\mathrm{x}10^{-12}\mathrm{m}, m_{He4} \to 3.41\mathrm{x}10^{-12}\mathrm{m}$ .

3. Lithium Li $(r_{6,7})$ $m_{Li6}\rightarrow 5.13\mathrm{x}10^{-12}\mathrm{m},m_{Li7}\rightarrow 5.98\mathrm{x}10^{-12}\mathrm{m}.$

Beryllium Be $(r_{8,9})$ $m_{Be8} \rightarrow 6.82x10^{-12}m$ , $m_{Be9} \rightarrow 7.68x10^{-12}m$ .
Boron B ( $r_{10.11}$ ) $m_{B10} \rightarrow 8.53 \times 10^{-12}$ m, $m_{B11} \rightarrow 9.38 \times 10^{-12}$ m.
Carbon C $(r_{12,13})$ $m_{C12} \to 1.02 \times 10^{-11} \mathrm{~m}, m_{C13} \to 1.11 \times 10^{-11} \mathrm{~m}$ .
Nitrogen N ( $r_{14,15}$ ) $m_{N14} \rightarrow 1.19x10^{-11}m$ , $m_{N15} \rightarrow 1.28x10^{-11}m$ .

Fluorine F ( $r_{19}$ ) $m_{F19} \rightarrow 1.62 \times 10^{-11}$ m.

11. Sodium Na $(r_{23})$ $m_{Na23}\rightarrow 1.96\mathrm{x}10^{-11}\mathrm{m}$

13. Aluminium Al $(r_{27})m_{Al27}\rightarrow 2.30\mathrm{x}10^{-11}\mathrm{m}.$

Silicon Si $(r_{28,29,30})$ $m_{Si28} \rightarrow 2.38x10^{-11}m$ , $m_{Si29} \rightarrow 2.47x10^{-11}m$ , $m_{Si30} \rightarrow 2.55x10^{-11}m$ .

15. Phosphorous P $(r_{31})m_{P31}\rightarrow 2.64\mathrm{x}10^{-11}\mathrm{m}.$

Sulphur S ( $r_{32,33,34,36}$ ) $m_{S32} \rightarrow 2.72x10^{-11}m$ , $m_{S33} \rightarrow 2.81x10^{-11}m$ , $m_{S34} \rightarrow 2.89x10^{-11}m$ , $m_{S36} \rightarrow 3.06x10^{-11}m$ .

17. Chlorine Cl $(r_{35,37})m_{Cl35}\rightarrow 2.98\mathrm{x}10^{-11}\mathrm{m},m_{Cl37}\rightarrow 3.15\mathrm{x}10^{-11}\mathrm{m}.$

m.

$m_{Pb208} \rightarrow 17.72 \times 10^{-11} \mathrm{~m}$ , which is the last of the Stable Nuclides.

Americium Am $(r_{241,242,243})$ $m_{Am241} \rightarrow 20.54 \times 10^{-11}$ m, $m_{Am242} \rightarrow 20.62 \times 10^{-11}$ m, $m_{Am243} \rightarrow 20.71 \times 10^{-11}$ m.

Berkelium Bk ( $r_{247}$ ) $m_{Bk247} \rightarrow 21.05 \times 10^{-11}$ m.
Californium Cf $(r_{249,250,251,252})$ $m_{Cf249} \rightarrow 21.22x10^{-11}m$ , $m_{Cf250} \rightarrow 21.31x10^{-11}m$ , $m_{Cf251} \rightarrow 21.39x10^{-11}m$ , $m_{Cf252} \rightarrow 21.48x10^{-11}m$ .
Einsteinium Es $(r_{252,253,254,255,256,257})$ $m_{Es252} \rightarrow 21.48x10^{-11}m$ , $m_{Es253} \rightarrow 21.56x10^{-11}m$ , $m_{Es254} \rightarrow$

Fermion Fm $(r_{253,257})$ $m_{Fm253} \rightarrow 21.56 \times 10^{-11}$ m, $m_{Fm257} \rightarrow 21.90 \times 10^{-11}$ m.
Mendelevium Md ( $r_{257,258,259,260}$ ) $m_{Md257} \rightarrow 21.90 \times 10^{-11}$ m, $m_{Md258} \rightarrow 21.99 \times 10^{-11}$ m, $m_{Md259} \rightarrow$

22.08x10 $^{-11}$ m, $m_{Md260} \rightarrow 22.16x10^{-11}$ m.

All nuclei beyond nuclear number 260 are very unstable (have very short half-lives) and therefore are not being considered. The same instability applies to nuclei numbers between 212 and 221 that will also be left out of the Table. The reason for the instability pertains to their large number and the way the protons and neutrons are situated within the nucleus. Since the nucleon binding forces act over short distances as the nucleus gets larger in size the binding forces which acts over only a few neighboring nucleons cannot compete with the longer range electrical repulsive forces between protons, hence the nucleus becomes unstable.

III. DENSITY CALCULATIONS

Density $(\rho) = \text{Mass/Volume} = \text{Mass} / (4\pi r^{3}/3)$ using the values of r from the Radius Calculations and the known values of Mass.

Electron $\rho = 2.12 \times 10^{15} \, \text{Kg/m}^3$ .

Electron Neutrino $\rho = 1.18x10^{26}$ Kg/m $^{3}$ .

Up Quark $\rho = 1.06x10^{14}$ Kg/m $^{3}$ .

Down Quark $\rho = 2.41 \times 10^{13}$ Kg/m $^{3}$ .

Proton and Neutron Density $\rho = 6.30 \times 10^{8}$ Kg/m $^{3}$ .

The Radius and Density Table of the Nucleons of the Periodic Table are used to correct the mistakes made in Physics Textbooks that all sized nuclei have the same Density (Reference 4) of $2.3 \times 10^{17}$ kg/m $^{3}$ based on the incorrect assumption that the radius of all nuclei is proportional to $A^{\frac{1}{3}}$ where A is their Mass Number, and therefore their Density is independent of their Mass Number.

. Within the Table S = Stable Nucleus and U = Unstable Nucleus. Simplifying the formula $\rho = M/V$ to: $\rho = (\text{No. of Nucleons x } 3.99 \times 10^{-28}) / r^{3} \, \text{Kg/m}^{3}$ we get:

Number of Nucleons.	Radius in m.	Density in $Kg/m^3$ .
1 H-S	$8.59x10^{-13}$	$6.30x10^8$
2 H-S	$1.72x10^{-12}$	$1.57x10^8$
3 He-S	$2.57x10^{-12}$	$7.05x10^7$
4 He-S	$3.41x10^{-12}$	$4.03x10^7$
5 ----	Does Not Exist.	----
6 Li-S	$5.13x10^{-12}$	$1.77x10^7$
7 Li-S	$5.98x10^{-12}$	$1.31x10^7$
8 Be-U	$6.82x10^{-12}$	$1.01x10^7$
9 Be-S	$7.68x10^{-12}$	$7.93x10^6$
10 B-S	$8.53x10^{-12}$	$6.43x10^6$
11 B-S	$9.38x10^{-12}$	$5.32x10^6$
12 C-S	$1.02x10^{-11}$	$4.51x10^6$
13 C-S	$1.11x10^{-11}$	$3.79x10^6$
14 N-S	$1.19x10^{-11}$	$3.31x10^6$
15 N-S	$1.28x10^{-11}$	$2.85x10^6$
16 O-S	$1.36x10^{-11}$	$2.54x10^6$
17 O-S	$1.45x10^{-11}$	$2.22x10^6$
18 O-S	$1.53x10^{-11}$	$2.01x10^6$
19 F-S	$1.62x10^{-11}$	$1.78x10^6$
20 Ne-S	$1.70x10^{-11}$	$1.62x10^6$
21 Ne-S	$1.79x10^{-11}$	$1.46x10^6$
22 Ne-S	$1.87x10^{-11}$	$1.34x10^6$
23 Na-S	$1.96x10^{-11}$	$1.22x10^6$
24 Mg-S	$2.04x10^{-11}$	$1.13x10^6$
25 Mg-S	$2.13x10^{-11}$	$1.03x10^6$
26 Mg-S	$2.21x10^{-11}$	$9.61x10^5$
27 Al-S	$2.30x10^{-11}$	$8.85x10^5$
28 Si-S	$2.38x10^{-11}$	$8.29x10^5$
29 Si-S	$2.47x10^{-11}$	$7.68x10^5$
30 Si-S	$2.55x10^{-11}$	$7.22x10^5$
31 P-S	$2.64x10^{-11}$	$6.72x10^5$
32 Sulphur-S	$2.72x10^{-11}$	$6.34x10^5$
33 Sulphur-S	$2.81x10^{-11}$	$5.93x10^5$
34 Sulphur-S	$2.89x10^{-11}$	$5.62x10^5$
35 Cl-S	$2.98 \times 10^{-11}$	$5.28 \times 10^{5}$
36Sulphur,Ar-S	$3.06 \times 10^{-11}$	$5.01 \times 10^{5}$
37 Cl-S	$3.15 \times 10^{-11}$	$4.72 \times 10^{5}$
38 Ar-S	$3.23 \times 10^{-11}$	$4.50 \times 10^{5}$
39 K-S	$3.32 \times 10^{-11}$	$4.25 \times 10^{5}$
40 Ar, Ca-S	$3.40 \times 10^{-11}$	$4.06 \times 10^{5}$
41 K-S	$3.49 \times 10^{-11}$	$3.85 \times 10^{5}$
42 Ca-S	$3.58 \times 10^{-11}$	$3.65 \times 10^{5}$
43 Ca-S	$3.66 \times 10^{-11}$	$3.50 \times 10^{5}$
44 Ca-S	$3.75 \times 10^{-11}$	$3.33 \times 10^{5}$
45 Sc-S	$3.83 \times 10^{-11}$	$3.20 \times 10^{5}$
46 Ca, Ti-S	$3.92 \times 10^{-11}$	$3.05 \times 10^{5}$
47 Ti-S	$4.00 \times 10^{-11}$	$2.93 \times 10^{5}$
48 Ti-S	$4.09 \times 10^{-11}$	$2.80 \times 10^{5}$
49 Ti-S	$4.17 \times 10^{-11}$	$2.70 \times 10^{5}$
50 Ti-S	$4.26 \times 10^{-11}$	$2.58 \times 10^{5}$
51 V-S	$4.34 \times 10^{-11}$	$2.49 \times 10^{5}$
52 Cr-S	$4.43 \times 10^{-11}$	$2.39 \times 10^{5}$
53 Cr-S	$4.51 \times 10^{-11}$	$2.31 \times 10^{5}$
54 Cr, Fe-S	$4.60 \times 10^{-11}$	$2.21 \times 10^{5}$
55 Mn-S	$4.68 \times 10^{-11}$	$2.14 \times 10^{5}$
56 Fe-S	$4.77 \times 10^{-11}$	$2.06 \times 10^{5}$
57 Fe-S	$4.85 \times 10^{-11}$	$1.99 \times 10^{5}$
58 Fe, Ni-S	$4.94 \times 10^{-11}$	$1.92 \times 10^{5}$
59 Co-S	$5.02 \times 10^{-11}$	$1.86 \times 10^{5}$
60 Ni-S	$5.11 \times 10^{-11}$	$1.79 \times 10^{5}$
61 Ni-S	$5.19 \times 10^{-11}$	$1.74 \times 10^{5}$
62 Ni-S	$5.28 \times 10^{-11}$	$1.68 \times 10^{5}$
63 Cu-S	$5.36 \times 10^{-11}$	$1.63 \times 10^{5}$
64 Ni, Zn-S	$5.45 \times 10^{-11}$	$1.58 \times 10^{5}$
65 Cu-S	$5.53 \times 10^{-11}$	$1.53 \times 10^{5}$
66 Zn-S	$5.62 \times 10^{-11}$	$1.48 \times 10^{5}$
67 Zn-S	$5.70 \times 10^{-11}$	$1.44 \times 10^{5}$
68 Zn-S	$5.79 \times 10^{-11}$	$1.40 \times 10^{5}$
69 Ga-S	$5.87 \times 10^{-11}$	$1.36 \times 10^{5}$
70 Zn, Ge-S	$5.96 \times 10^{-11}$	$1.32 \times 10^{5}$
71 Ga-S	$6.04 \times 10^{-11}$	$1.29 \times 10^{5}$
72 Ge-S	$6.13 \times 10^{-11}$	$1.25 \times 10^{5}$
73 Ge-S	$6.21 \times 10^{-11}$	$1.22 \times 10^{5}$
74 Ge, Se-S	$6.30 \times 10^{-11}$	$1.18 \times 10^{5}$
75 As-S	$6.38 \times 10^{-11}$	$1.15 \times 10^{5}$
76 Ge, Se-S	$6.47 \times 10^{-11}$	$1.12 \times 10^{5}$
77 Se-S	$6.55 \times 10^{-11}$	$1.09 \times 10^{5}$
78 Se-S	$6.64 \times 10^{-11}$	$1.06 \times 10^{5}$
79 Br-S	$6.72 \times 10^{-11}$	$1.04 \times 10^{5}$
80 Se, Kr-S	$6.81 \times 10^{-11}$	$1.01 \times 10^{5}$
81 Br-S	$6.89 \times 10^{-11}$	$9.88 \times 10^{4}$
82 Kr-S	$6.98 \times 10^{-11}$	$9.62 \times 10^{4}$
83 Kr-S	$7.06 \times 10^{-11}$	$9.41 \times 10^{4}$
84 Kr, Sr-S	$7.15 \times 10^{-11}$	$9.17 \times 10^{4}$
85 Rb-S	$7.23 \times 10^{-11}$	$8.97 \times 10^{4}$
86 Kr, Sr-S	$7.32 \times 10^{-11}$	$8.75 \times 10^{4}$
87 Sr-S	$7.40 \times 10^{-11}$	$8.57 \times 10^{4}$
88 Sr-S	$7.49 \times 10^{-11}$	$8.36 \times 10^{4}$
89 Y-S	$7.57 \times 10^{-11}$	$8.19 \times 10^{4}$
90 Zr-S	$7.66 \times 10^{-11}$	$7.99 \times 10^{4}$
91 Zr-S	$7.75 \times 10^{-11}$	$7.80 \times 10^{4}$
92 Zr, Mo-S	$7.83 \times 10^{-11}$	$7.65 \times 10^{4}$
93 Nb-S	$7.92 \times 10^{-11}$	$7.47 \times 10^{4}$
94 Zr, Mo-S	$8.00 \times 10^{-11}$	$7.33 \times 10^{4}$
95 Mo-S	$8.09 \times 10^{-11}$	$7.16 \times 10^{4}$
96 Mo, Ru-S	$8.17 \times 10^{-11}$	$7.02 \times 10^{4}$
97 Mo-S	$8.26 \times 10^{-11}$	$6.87 \times 10^{4}$
98 Mo, Ru-S	$8.34 \times 10^{-11}$	$6.74 \times 10^{4}$
99 Tc-U, Ru-S	$8.43 \times 10^{-11}$	$6.59 \times 10^{4}$
100 Ru-S	$8.51 \times 10^{-11}$	$6.47 \times 10^{4}$
101 Ru-S	$8.60 \times 10^{-11}$	$6.34 \times 10^{4}$
102 Ru, Pd-S	$8.68 \times 10^{-11}$	$6.22 \times 10^{4}$
103 Rh-S	$8.77 \times 10^{-11}$	$6.09 \times 10^{4}$
104 Ru, Pd-S	$8.86 \times 10^{-11}$	$5.97 \times 10^{4}$
105 Pd-S	$8.94 \times 10^{-11}$	$5.86 \times 10^{4}$
106 Pd, Cd-S	$9.02 \times 10^{-11}$	$5.76 \times 10^{4}$
107 Ag-S	$9.11 \times 10^{-11}$	$5.65 \times 10^{4}$
108 Pd, Cd-S	$9.19 \times 10^{-11}$	$5.55 \times 10^{4}$
109 Ag-S	$9.28 \times 10^{-11}$	$5.44 \times 10^{4}$
110 Pd, Cd-S	$9.36 \times 10^{-11}$	$5.35 \times 10^{4}$
111 Cd-S	$9.45 \times 10^{-11}$	$5.25 \times 10^{4}$
112 Cd, Sn-S	$9.53 \times 10^{-11}$	$5.16 \times 10^{4}$
113 In-S	$9.62 \times 10^{-11}$	$5.06 \times 10^{4}$
114 Cd, Sn-S	$9.70 \times 10^{-11}$	$4.98 \times 10^{4}$
115 Sn-S	$9.79 \times 10^{-11}$	$4.89 \times 10^{4}$
116 Sn-S	$9.88 \times 10^{-11}$	$4.80 \times 10^{4}$
117 Sn-S	$9.96 \times 10^{-11}$	$4.72 \times 10^{4}$
118 Sn-S	$10.05 \times 10^{-11}$	$4.64 \times 10^{4}$
119 Sn-S	$10.13 \times 10^{-11}$	$4.57 \times 10^{4}$
120 Sn, Te-S	$10.22 \times 10^{-11}$	$4.49 \times 10^{4}$
121 Sb-S	$10.30 \times 10^{-11}$	$4.42 \times 10^{4}$
122 Sn, Te-S	$10.39 \times 10^{-11}$	$4.34 \times 10^{4}$
123 Sb-S	$10.47 \times 10^{-11}$	$4.28 \times 10^{4}$
124 Sn,Te,Xe-S	$10.56 \times 10^{-11}$	$4.20 \times 10^{4}$
125 Te-S	$10.64 \times 10^{-11}$	$4.14 \times 10^{4}$
126 Te, Xe-S	$10.73 \times 10^{-11}$	$4.07 \times 10^{4}$
127 I-S	$10.81 \times 10^{-11}$	$4.01 \times 10^{4}$
128 Xe-S	$10.91 \times 10^{-11}$	$3.93 \times 10^{4}$
129 Xe-S	$10.98 \times 10^{-11}$	$3.89 \times 10^{4}$
130 Xe, Ba-S	$11.07 \times 10^{-11}$	$3.82 \times 10^{4}$
131 Xe-S	$11.15 \times 10^{-11}$	$3.77 \times 10^{4}$
132 Xe, Ba-S	$11.24 \times 10^{-11}$	$3.71 \times 10^{4}$
133 Cs-S	$11.32 \times 10^{-11}$	$3.66 \times 10^{4}$
134 Xe, Ba-S	$11.41 \times 10^{-11}$	$3.60 \times 10^{4}$
135 Ba-S	$11.49 \times 10^{-11}$	$3.55 \times 10^{4}$
136 Ba, Ce-S	$11.58 \times 10^{-11}$	$3.49 \times 10^{4}$
137 Ba-S	$11.66x10^{-11}$	$3.45x10^{4}$
138 Ba, Ce-S	$11.75x10^{-11}$	$3.39x10^{4}$
139 La-S	$11.83x10^{-11}$	$3.35x10^{4}$
140 Ce-S	$11.92x10^{-11}$	$3.30x10^{4}$
141 Pr-S	$12.01x10^{-11}$	$3.25x10^{4}$
142 Nd-S	$12.09x10^{-11}$	$3.21x10^{4}$
143 Nd-S	$12.18x10^{-11}$	$3.16x10^{4}$
144 Sm-S	$12.26x10^{-11}$	$3.12x10^{4}$
145 Nd-S	$12.35x10^{-11}$	$3.07x10^{4}$
146 Nd-S	$12.43x10^{-11}$	$3.03x10^{4}$
147 Pm-U	$12.52x10^{-11}$	$2.99x10^{4}$
148 Nd-S	$12.60x10^{-11}$	$2.95x10^{4}$
149 Sm-U	$12.69x10^{-11}$	$2.91x10^{4}$
150 Sm-S	$12.77x10^{-11}$	$2.87x10^{4}$
151 Eu-S	$12.86x10^{-11}$	$2.83x10^{4}$
152 Sm-S	$12.94x10^{-11}$	$2.80x10^{4}$
153 Eu-S	$13.03x10^{-11}$	$2.76x10^{4}$
154 Sm, Gd-S	$13.11x10^{-11}$	$2.73x10^{4}$
155 Gd-S	$13.20x10^{-11}$	$2.69x10^{4}$
156 Gd, Dy-S	$13.28x10^{-11}$	$2.66x10^{4}$
157 Gd-S	$13.37x10^{-11}$	$2.62x10^{4}$
158 Gd, Dy-S	$13.46x10^{-11}$	$2.59x10^{4}$
159 Tb-S	$13.54x10^{-11}$	$2.56x10^{4}$
160 Gd, Dy-S	$13.63x10^{-11}$	$2.52x10^{4}$
161 Dy-S	$13.71x10^{-11}$	$2.49x10^{4}$
162 Dy, Er-S	$13.80x10^{-11}$	$2.46x10^{4}$
163 Dy-S	$13.88x10^{-11}$	$2.43x10^{4}$
164 Dy, Er-S	$13.97x10^{-11}$	$2.40x10^{4}$
165 Ho-S	$14.05x10^{-11}$	$2.37x10^{4}$
166 Er-S	$14.14x10^{-11}$	$2.34x10^{4}$
167 Er-S	$14.22x10^{-11}$	$2.32x10^{4}$
168 Er, Yb-S	$14.31x10^{-11}$	$2.29x10^{4}$
169 Tm-S	$14.39 \times 10^{-11}$	$2.26 \times 10^{4}$
170 Er, Yb-S	$14.48 \times 10^{-11}$	$2.23 \times 10^{4}$
171 Yb-S	$14.56 \times 10^{-11}$	$2.21 \times 10^{4}$
172 Yb-S	$14.65 \times 10^{-11}$	$2.18 \times 10^{4}$
173 Yb-S	$14.73 \times 10^{-11}$	$2.16 \times 10^{4}$
174 Yb-S	$14.82 \times 10^{-11}$	$2.13 \times 10^{4}$
175 Lu-S	$14.90 \times 10^{-11}$	$2.11 \times 10^{4}$
176 Yb, Hf-S	$14.99 \times 10^{-11}$	$2.08 \times 10^{4}$
177 Hf-S	$15.08 \times 10^{-11}$	$2.06 \times 10^{4}$
178 Hf-S	$15.16 \times 10^{-11}$	$2.04 \times 10^{4}$
179 Hf-S	$15.25 \times 10^{-11}$	$2.01 \times 10^{4}$
180 Hf, W-S	$15.33 \times 10^{-11}$	$1.99 \times 10^{4}$
181 Ta-S	$15.42 \times 10^{-11}$	$1.97 \times 10^{4}$
182 W-S	$15.50 \times 10^{-11}$	$1.95 \times 10^{4}$
183 W-S	$15.59 \times 10^{-11}$	$1.93 \times 10^{4}$
184 W, Os-S	$15.67 \times 10^{-11}$	$1.91 \times 10^{4}$
185 W, Re-S	$15.76 \times 10^{-11}$	$1.89 \times 10^{4}$
186 Os-U	$15.84 \times 10^{-11}$	$1.87 \times 10^{4}$
187 Re-U, Os-S	$15.93 \times 10^{-11}$	$1.85 \times 10^{4}$
188 Os-S	$16.01 \times 10^{-11}$	$1.83 \times 10^{4}$
189 Os-S	$16.10 \times 10^{-11}$	$1.81 \times 10^{4}$
190 Os-S	$16.18 \times 10^{-11}$	$1.79 \times 10^{4}$
191 Ir-S	$16.27 \times 10^{-11}$	$1.77 \times 10^{4}$
192 Os, Pt-S	$16.36 \times 10^{-11}$	$1.75 \times 10^{4}$
193 Ir-S	$16.44 \times 10^{-11}$	$1.73 \times 10^{4}$
194 Pt-S	$16.53 \times 10^{-11}$	$1.71 \times 10^{4}$
195 Pt-S	$16.61 \times 10^{-11}$	$1.70 \times 10^{4}$
196 Pt, Hg-S	$16.70 \times 10^{-11}$	$1.68 \times 10^{4}$
197 Au-S	$16.78 \times 10^{-11}$	$1.66 \times 10^{4}$
198 Pt, Hg-S	$16.87 \times 10^{-11}$	$1.65 \times 10^{4}$
199 Hg-S	$16.95 \times 10^{-11}$	$1.63 \times 10^{4}$
200 Hg-S	$17.04 \times 10^{-11}$	$1.61 \times 10^{4}$
201 Hg-S	$17.12x10^{-11}$	$1.60x10^{4}$
202 Hg-S	$17.21x10^{-11}$	$1.58x10^{4}$
203 Tl-S	$17.29x10^{-11}$	$1.57x10^{4}$
204 Hg-S	$17.38x10^{-11}$	$1.55x10^{4}$
205 Tl-S	$17.46x10^{-11}$	$1.54x10^{4}$
206 Pb-S	$17.55x10^{-11}$	$1.52x10^{4}$
207 Pb-S, At-U	$17.63x10^{-11}$	$1.51x10^{4}$
208 Pb-S; All nuclei > 208 are Unstable.	$17.72x10^{-11}$	$1.49x10^{4}$
209Bi, Po, At-U	$17.81x10^{-11}$	$1.48x10^{4}$
210 At-U	$17.89x10^{-11}$	$1.46x10^{4}$
211 At-U	$17.98x10^{-11}$	$1.45x10^{4}$
222 Rn-U	$18.92x10^{-11}$	$1.31x10^{4}$
223 Fr-U	$19.01x10^{-11}$	$1.30x10^{4}$
224 Fr-U	$19.09x10^{-11}$	$1.28x10^{4}$
225 Fr-U	$19.17x10^{-11}$	$1.27x10^{4}$
226 Ra-U	$19.26x10^{-11}$	$1.26x10^{4}$
227 Ac-U	$19.34x10^{-11}$	$1.25x10^{4}$
228 Ra-U	$19.43x10^{-11}$	$1.24x10^{4}$
229 Th-U	$19.51x10^{-11}$	$1.23x10^{4}$
230 Th-U	$19.60x10^{-11}$	$1.22x10^{4}$
231 Pa-U	$19.68x10^{-11}$	$1.21x10^{4}$
232 Th, Ur-U	$19.77x10^{-11}$	$1.20x10^{4}$
233 Ur-U	$19.86x10^{-11}$	$1.19x10^{4}$
234 Ur-U	$19.94x10^{-11}$	$1.18x10^{4}$
235 Ur-U	$20.03x10^{-11}$	$1.17x10^{4}$
236Ur,Np,Pu-U	$20.11x10^{-11}$	$1.16x10^{4}$
237 Ur, Np-U	$20.20x10^{-11}$	$1.15x10^{4}$
238 Ur, Pu-U	$20.28x10^{-11}$	$1.14x10^{4}$
239 Pu-U	$20.37x10^{-11}$	$1.13x10^{4}$
240 Pu-U	$20.45x10^{-11}$	$1.12x10^{4}$
241 Pu, Am-U	$20.54x10^{-11}$	$1.11x10^{4}$
242 Pu, Am-U	$20.62x10^{-11}$	$1.10x10^{4}$
243 Am-U	$20.71x10^{-11}$	$1.09x10^{4}$
244 Pu-U	$20.79x10^{-11}$	$1.08x10^{4}$
245 Cm-U	$20.88x10^{-11}$	$1.074x10^{4}$
246 Cm-U	$20.96x10^{-11}$	$1.066x10^{4}$
247 Cm, Bk-U	$21.05x10^{-11}$	$1.06x10^{4}$
248 Cm-U	$21.14x10^{-11}$	$1.05x10^{4}$
249 Cf-U	$21.22x10^{-11}$	$1.04x10^{4}$
250 Cf-U	$21.31x10^{-11}$	$1.03x10^{4}$
251 Cf-U	$21.39x10^{-11}$	$1.02x10^{4}$
252 Cf, Es-U	$21.48x10^{-11}$	$1.01x10^{4}$
253 Es, Fm-U	$21.56x10^{-11}$	$10.07x10^{3}$
254 Es-U	$21.64x10^{-11}$	$10.00x10^{3}$
255 Es-U	$21.73x10^{-11}$	$9.92x10^{3}$
256 Es-U	$21.82x10^{-11}$	$9.83x10^{3}$
257 Es, Fm, Md-U	$21.90x10^{-11}$	$9.76x10^{3}$
258 Md-U	$21.99x10^{-11}$	$9.68x10^{3}$
259 Md-U	$22.08x10^{-11}$	$9.60x10^{3}$
260 Md-U	$22.16x10^{-11}$	$9.53x10^{3}$

IV. CONCLUSION

All the radii of the elementary particles are fundamental and therefore they should be included, along with the radii and charges of the three neutrinos, in the Table at the end of a University Physics Book in conjunction with the other Physical Constants of nature. The sizes of the nuclei of the elements depend only on the total number of nucleons. If there is an overlap of the number of nucleons between two or more elements their size will be the same. As an example, Barium, Lanthanum, and Cesium can all carry 138 nucleons of the same radius of $11.75 \times 10^{-11}$ m. Another example would be Hafnium carrying 176 nucleons of radius $14.99 \times 10^{-11}$ m with Ytterbium and Lutetium; and Hafnium carrying 180 nucleons of radius $15.33 \times 10^{-11}$ m with Tantalum and Tungsten. The radii and densities of all the nuclei of all the elements of the Periodic Table should be included in Chemistry Textbooks. Densities decrease as the number of nucleons and their radii increase. The strong nuclear attractive force between the nucleons that is short ranged begins to become weaker than the repulsive electric force between the protons that is long ranged until nucleons with higher mass number become unstable.

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The datasets used in this study are openly available at [repository link] and the source code is available on GitHub at [GitHub link].

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Online published 4 April 2025

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density Down Quark electron Electron Neutrino Neutron Proton Radius Table of Nuclear radiuses and densities. Up Quark

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The Radii and Densities of Elementary Particles and Periodic Table Nucleons

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The Radii and Densities of Elementary Particles and Periodic Table Nucleons

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I. INTRODUCTION

II. RADIUS CALCULATIONS

1. Hydrogen H ( r 1 , 2 ) m H 1 → 8.59 x 10 − 13 m , m H 2 → 1.72 x 10 − 12 m .

3. Lithium Li ( r 6 , 7 ) m L i 6 → 5.13 x 10 − 12 m , m L i 7 → 5.98 x 10 − 12 m .

11. Sodium Na ( r 23 ) m N a 23 → 1.96 x 10 − 11 m

13. Aluminium Al ( r 27 ) m A l 27 → 2.30 x 10 − 11 m .

15. Phosphorous P ( r 31 ) m P 31 → 2.64 x 10 − 11 m .

17. Chlorine Cl ( r 35 , 37 ) m C l 35 → 2.98 x 10 − 11 m , m C l 37 → 3.15 x 10 − 11 m .

22.08x10 − 11 m, m M d 260 → 22.16 x 10 − 11 m.

III. DENSITY CALCULATIONS

IV. CONCLUSION

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