v0+1 · built electron by electron · Z = 169 → 366 · model only past Z ≈ 170
Out to 366: where the rows close
Same method as the first build (element-168-build.html): each atom finds its own lowest-energy arrangement, with nothing assigned by a filling rule. This page runs from 169 to 366. Past Z ≈ 170 the innermost electron has dropped below the floor of empty space, so everything here is model-only : atoms this heavy cannot hold this form. AMBER throughout
The build, row by row
169: newest electron 9s, gap 0.51 eV, settled, code 144+21+3+1 170: newest electron 9s, gap 0.58 eV, did not settle, code 144+21+5 170 171: newest electron 7f, gap 0.15 eV, did not settle, code 144+21+5+1 172: newest electron 7f, gap 0.46 eV, did not settle, code 144+21+5+2 173: newest electron 6g, gap 1.48 eV, did not settle, code 144+21+8 174: newest electron 6g, gap 2.41 eV, did not settle, code 144+21+8+1 175: newest electron 6g, gap 0.10 eV, did not settle, code 144+21+8+2 176: newest electron 6g, gap 6.38 eV, did not settle, code 144+21+8+3 177: newest electron 6g, gap 3.37 eV, did not settle, code 144+21+8+3+1 178: newest electron 6g, gap 2.03 eV, did not settle, code 144+34 179: newest electron 6g, gap 9.60 eV, did not settle, code 144+34+1 180: newest electron 6g, gap 1.78 eV, did not settle, code 144+34+2 180 181: newest electron 9p, gap 0.42 eV, did not settle, code 144+34+3 182: newest electron 6g, gap 2.23 eV, did not settle, code 144+34+3+1 183: newest electron 9p, gap 0.79 eV, did not settle, code 144+34+5 184: newest electron 8p, gap 7.81 eV, did not settle, code 144+34+5+1 185: newest electron 9p, gap 0.72 eV, did not settle, code 144+34+5+2 186: newest electron 6g, gap 2.12 eV, did not settle, code 144+34+8 187: newest electron 9s, gap 0.94 eV, settled, code 144+34+8+1 188: newest electron 7f, gap 0.18 eV, did not settle, code 144+34+8+2 189: newest electron 7f, gap 0.35 eV, did not settle, code 144+34+8+3 190: newest electron 7f, gap 0.68 eV, did not settle, code 144+34+8+3+1 190 191: newest electron 7f, gap 0.16 eV, did not settle, code 144+34+13 192: newest electron 7f, gap 0.50 eV, did not settle, code 144+34+13+1 193: newest electron 7f, gap 0.33 eV, did not settle, code 144+34+13+2 194: newest electron 7f, gap 0.30 eV, did not settle, code 144+34+13+3 195: newest electron 7f, gap 0.24 eV, settled, code 144+34+13+3+1 196: newest electron 7f, gap 0.82 eV, settled, code 144+34+13+5 197: newest electron 7f, gap 1.41 eV, settled, code 144+34+13+5+1 198: newest electron 7f, gap 2.00 eV, settled, code 144+34+13+5+2 199: newest electron 7f, gap 2.61 eV, settled, code 144+55 200: newest electron 7f, gap 3.22 eV, settled, code 144+55+1 200 201: newest electron 9s, gap 1.32 eV, settled, code 144+55+2 202: newest electron 9s, gap 0.35 eV, settled, code 144+55+3 203: newest electron 8d, gap 1.79 eV, did not settle, code 144+55+3+1 204: newest electron 8d, gap 1.71 eV, did not settle, code 144+55+5 205: newest electron 8d, gap 0.29 eV, settled, code 144+55+5+1 206: newest electron 8d, gap 0.83 eV, settled, code 144+55+5+2 207: newest electron 8d, gap 1.38 eV, settled, code 144+55+8 208: newest electron 8d, gap 1.95 eV, settled, code 144+55+8+1 209: newest electron 8d, gap 2.53 eV, settled, code 144+55+8+2 210: newest electron 8d, gap 3.12 eV, settled, code 144+55+8+3 210 211: newest electron 9s, gap 2.54 eV, settled, code 144+55+8+3+1 212: newest electron 9s, gap 2.97 eV, settled, code 144+55+13 213: newest electron 9p, gap 2.37 eV, settled, code 144+55+13+1 214: newest electron 9p, gap 3.16 eV, settled, code 144+55+13+2 215: newest electron 9p, gap 3.94 eV, settled, code 144+55+13+3 216: newest electron 9p, gap 4.69 eV, settled, code 144+55+13+3+1 217: newest electron 9p, gap 5.44 eV, settled, code 144+55+13+5 218: newest electron 9p, gap 6.19 eV, settled, code 144+55+13+5+1 218 219: newest electron 10s, gap 0.01 eV, did not settle, code 144+55+13+5+2 220: newest electron 7g, gap 0.94 eV, did not settle, code 144+55+21 220 221: newest electron 7g, gap 1.50 eV, did not settle, code 144+55+21+1 222: newest electron 7g, gap 0.21 eV, did not settle, code 144+55+21+2 223: newest electron 7g, gap 0.12 eV, did not settle, code 144+55+21+3 224: newest electron 6h, gap 6.87 eV, did not settle, code 144+55+21+3+1 225: newest electron 6h, gap 3.64 eV, did not settle, code 144+55+21+5 226: newest electron 7g, gap 0.90 eV, did not settle, code 144+55+21+5+1 227: newest electron 8f, gap 0.56 eV, did not settle, code 144+55+21+5+2 228: newest electron 9d, gap 0.05 eV, did not settle, code 144+55+21+8 229: newest electron 8f, gap 0.46 eV, did not settle, code 144+55+21+8+1 230: newest electron 8f, gap 0.63 eV, did not settle, code 144+55+21+8+2 230 231: newest electron 8f, gap 0.75 eV, did not settle, code 144+55+21+8+3 232: newest electron 10p, gap 0.67 eV, did not settle, code 144+55+21+8+3+1 233: newest electron 10p, gap 0.50 eV, did not settle, code 233 234: newest electron 6h, gap 5.02 eV, did not settle, code 233+1 235: newest electron 7g, gap 3.13 eV, did not settle, code 233+2 236: newest electron 9p, gap 0.97 eV, did not settle, code 233+3 237: newest electron 9p, gap 2.54 eV, did not settle, code 233+3+1 238: newest electron 7g, gap 1.33 eV, did not settle, code 233+5 239: newest electron 7g, gap 1.24 eV, did not settle, code 233+5+1 240: newest electron 6h, gap 7.91 eV, did not settle, code 233+5+2 240 241: newest electron 8f, gap 0.30 eV, did not settle, code 233+8 242: newest electron 8f, gap 0.33 eV, did not settle, code 233+8+1 243: newest electron 8f, gap 0.21 eV, did not settle, code 233+8+2 244: newest electron 8f, gap 0.48 eV, did not settle, code 233+8+3 245: newest electron 7g, gap 0.83 eV, did not settle, code 233+8+3+1 246: newest electron 7g, gap 2.00 eV, did not settle, code 233+13 247: newest electron 7g, gap 1.37 eV, did not settle, code 233+13+1 248: newest electron 9d, gap 0.10 eV, did not settle, code 233+13+2 249: newest electron 7g, gap 8.20 eV, did not settle, code 233+13+3 250: newest electron 7g, gap 3.98 eV, did not settle, code 233+13+3+1 250 251: newest electron 7g, gap 2.13 eV, did not settle, code 233+13+5 252: newest electron 7g, gap 3.14 eV, did not settle, code 233+13+5+1 253: newest electron 7g, gap 0.60 eV, did not settle, code 233+13+5+2 254: newest electron 7g, gap 2.93 eV, did not settle, code 233+21 255: newest electron 9p, gap 10.01 eV, did not settle, code 233+21+1 256: newest electron 9p, gap 7.24 eV, did not settle, code 233+21+2 257: newest electron 7g, gap 4.35 eV, did not settle, code 233+21+3 258: newest electron 7g, gap 0.02 eV, settled, code 233+21+3+1 259: newest electron 10s, gap 0.82 eV, settled, code 233+21+5 260: newest electron 8f, gap 0.09 eV, did not settle, code 233+21+5+1 260 261: newest electron 8f, gap 0.27 eV, did not settle, code 233+21+5+2 262: newest electron 8f, gap 0.39 eV, did not settle, code 233+21+8 263: newest electron 8f, gap 0.94 eV, did not settle, code 233+21+8+1 264: newest electron 8f, gap 1.16 eV, did not settle, code 233+21+8+2 265: newest electron 8f, gap 1.86 eV, did not settle, code 233+21+8+3 266: newest electron 8f, gap 0.60 eV, settled, code 233+21+8+3+1 267: newest electron 8f, gap 1.21 eV, settled, code 233+34 268: newest electron 8f, gap 1.83 eV, settled, code 233+34+1 269: newest electron 8f, gap 2.45 eV, settled, code 233+34+2 270: newest electron 8f, gap 3.08 eV, settled, code 233+34+3 270 271: newest electron 8f, gap 3.71 eV, settled, code 233+34+3+1 272: newest electron 8f, gap 4.34 eV, settled, code 233+34+5 273: newest electron 10s, gap 1.18 eV, settled, code 233+34+5+1 274: newest electron 10s, gap 0.08 eV, settled, code 233+34+5+2 275: newest electron 9d, gap 1.53 eV, did not settle, code 233+34+8 276: newest electron 9d, gap 0.01 eV, settled, code 233+34+8+1 277: newest electron 9d, gap 0.53 eV, settled, code 233+34+8+2 278: newest electron 9d, gap 1.06 eV, settled, code 233+34+8+3 279: newest electron 9d, gap 1.61 eV, settled, code 233+34+8+3+1 280: newest electron 9d, gap 2.16 eV, settled, code 233+34+13 280 281: newest electron 9d, gap 2.73 eV, settled, code 233+34+13+1 282: newest electron 9d, gap 3.30 eV, settled, code 233+34+13+2 283: newest electron 10s, gap 2.41 eV, settled, code 233+34+13+3 284: newest electron 10s, gap 2.81 eV, settled, code 233+34+13+3+1 285: newest electron 10p, gap 2.36 eV, settled, code 233+34+13+5 286: newest electron 10p, gap 3.12 eV, settled, code 233+34+13+5+1 287: newest electron 10p, gap 3.86 eV, settled, code 233+34+13+5+2 288: newest electron 10p, gap 4.58 eV, settled, code 233+55 289: newest electron 10p, gap 5.29 eV, settled, code 233+55+1 290: newest electron 10p, gap 6.00 eV, settled, code 233+55+2 290 291: newest electron 8g, gap 0.04 eV, did not settle, code 233+55+3 292: newest electron 8g, gap 1.99 eV, did not settle, code 233+55+3+1 293: newest electron 8g, gap 0.89 eV, did not settle, code 233+55+5 294: newest electron 7h, gap 1.97 eV, did not settle, code 233+55+5+1 295: newest electron 7h, gap 0.29 eV, did not settle, code 233+55+5+2 296: newest electron 7h, gap 1.45 eV, did not settle, code 233+55+8 297: newest electron 10d, gap 0.23 eV, did not settle, code 233+55+8+1 298: newest electron 7h, gap 3.18 eV, did not settle, code 233+55+8+2 299: newest electron 7h, gap 0.14 eV, did not settle, code 233+55+8+3 300: newest electron 7h, gap 3.99 eV, did not settle, code 233+55+8+3+1 300 301: newest electron 7h, gap 4.41 eV, did not settle, code 233+55+13 302: newest electron 9f, gap 0.20 eV, did not settle, code 233+55+13+1 303: newest electron 9f, gap 0.94 eV, did not settle, code 233+55+13+2 304: newest electron 7h, gap 17.84 eV, did not settle, code 233+55+13+3 305: newest electron 10s, gap 6.31 eV, did not settle, code 233+55+13+3+1 306: newest electron 10s, gap 4.41 eV, did not settle, code 233+55+13+5 307: newest electron 8g, gap 0.07 eV, did not settle, code 233+55+13+5+1 308: newest electron 7h, gap 4.88 eV, did not settle, code 233+55+13+5+2 309: newest electron 10p, gap 6.66 eV, did not settle, code 233+55+21 310: newest electron 8g, gap 2.06 eV, did not settle, code 233+55+21+1 310 311: newest electron 10p, gap 3.50 eV, did not settle, code 233+55+21+2 312: newest electron 7h, gap 0.46 eV, did not settle, code 233+55+21+3 313: newest electron 9f, gap 0.07 eV, did not settle, code 233+55+21+3+1 314: newest electron 8g, gap 0.71 eV, did not settle, code 233+55+21+5 315: newest electron 8g, gap 0.52 eV, did not settle, code 233+55+21+5+1 316: newest electron 8g, gap 3.10 eV, did not settle, code 233+55+21+5+2 317: newest electron 8g, gap 1.49 eV, did not settle, code 233+55+21+8 318: newest electron 8g, gap 0.58 eV, did not settle, code 233+55+21+8+1 319: newest electron 8g, gap 0.61 eV, did not settle, code 233+55+21+8+2 320: newest electron 8g, gap 0.27 eV, settled, code 233+55+21+8+3 320 321: newest electron 8g, gap 1.16 eV, settled, code 233+55+21+8+3+1 322: newest electron 8g, gap 2.04 eV, settled, code 233+89 323: newest electron 8g, gap 2.91 eV, settled, code 233+89+1 324: newest electron 8g, gap 7.73 eV, did not settle, code 233+89+2 325: newest electron 8g, gap 4.63 eV, settled, code 233+89+3 326: newest electron 8g, gap 5.48 eV, settled, code 233+89+3+1 327: newest electron 8g, gap 6.33 eV, settled, code 233+89+5 328: newest electron 8g, gap 4.95 eV, did not settle, code 233+89+5+1 329: newest electron 8g, gap 5.79 eV, did not settle, code 233+89+5+2 330: newest electron 10p, gap 6.81 eV, settled, code 233+89+8 330 331: newest electron 11s, gap 0.47 eV, settled, code 233+89+8+1 332: newest electron 9f, gap 0.12 eV, did not settle, code 233+89+8+2 333: newest electron 9f, gap 0.54 eV, did not settle, code 233+89+8+3 334: newest electron 9f, gap 0.28 eV, did not settle, code 233+89+8+3+1 335: newest electron 9f, gap 0.37 eV, settled, code 233+89+13 336: newest electron 9f, gap 1.04 eV, settled, code 233+89+13+1 337: newest electron 9f, gap 1.70 eV, settled, code 233+89+13+2 338: newest electron 9f, gap 2.35 eV, settled, code 233+89+13+3 339: newest electron 9f, gap 3.00 eV, settled, code 233+89+13+3+1 340: newest electron 9f, gap 3.66 eV, settled, code 233+89+13+5 340 341: newest electron 9f, gap 4.31 eV, settled, code 233+89+13+5+1 342: newest electron 9f, gap 4.96 eV, settled, code 233+89+13+5+2 343: newest electron 9f, gap 5.61 eV, settled, code 233+89+21 344: newest electron 9f, gap 6.27 eV, settled, code 233+89+21+1 345: newest electron 11s, gap 0.82 eV, settled, code 233+89+21+2 346: newest electron 11s, gap 0.07 eV, did not settle, code 233+89+21+3 347: newest electron 10d, gap 1.42 eV, did not settle, code 233+89+21+3+1 348: newest electron 10d, gap 0.36 eV, settled, code 233+89+21+5 349: newest electron 10d, gap 0.88 eV, settled, code 233+89+21+5+1 350: newest electron 10d, gap 1.41 eV, settled, code 233+89+21+5+2 350 351: newest electron 10d, gap 1.94 eV, settled, code 233+89+21+8 352: newest electron 10d, gap 2.48 eV, settled, code 233+89+21+8+1 353: newest electron 10d, gap 3.03 eV, settled, code 233+89+21+8+2 354: newest electron 10d, gap 3.58 eV, settled, code 233+89+21+8+3 355: newest electron 11s, gap 2.20 eV, settled, code 233+89+21+8+3+1 356: newest electron 11s, gap 2.57 eV, settled, code 233+89+34 357: newest electron 11p, gap 2.34 eV, settled, code 233+89+34+1 358: newest electron 11p, gap 3.06 eV, settled, code 233+89+34+2 359: newest electron 11p, gap 3.76 eV, settled, code 233+89+34+3 360: newest electron 11p, gap 4.44 eV, settled, code 233+89+34+3+1 360 361: newest electron 11p, gap 5.11 eV, settled, code 233+89+34+5 362: newest electron 11p, gap 4.65 eV, did not settle, code 233+89+34+5+1 362 363: newest electron 7i, gap 2.61 eV, did not settle, code 233+89+34+5+2 364: newest electron 7i, gap 4.18 eV, did not settle, code 233+89+34+8 365: newest electron 11d, gap 0.32 eV, did not settle, code 233+89+34+8+1 366: newest electron 11d, gap 0.19 eV, did not settle, code 233+89+34+8+2
s p d f g h itall = p shell closes · outlined = any subshell closes · faded = did not settle · ● = no 1 in the Fibonacci code
198 atoms built. 114 of them did not settle — more than half. The solver keeps swapping electrons between near-equal g, h, f and i levels. Only the settled atoms carry weight; the closures at the end of each row settled best. Colours are my legend and carry no physical meaning.
The closures
Z closes gap settled Fibonacci code ruler row rule
218 9p⁶ 6.19 eV yes 144+55+13+5+1 miss yes 290 10p⁶ 6.00 eV yes 233+55+2 hit yes 330 10p⁶ 6.81 eV yes 233+89+8 hit no 362 11p⁶ 4.65 eV no 233+89+34+5+1 miss yes
218, 290 and 362 close where the row rule 2⌈(k+1)/2⌉² says they should. 218 and 290 settled cleanly with gaps of about 6 eV. 362 closed its 11p shell, but its inner shells never settled. LIT (model)
The ruler misses 218 and 362, and both close anyway. These are your empty ones that close: they carry the 1 in their code. Here the Fibonacci ruler and the model atom disagree for the first time, and the atom wins. DEAD: the ruler as a rule for closures AMBER: the pattern (every other row misses from row 9 on)
330 is an extra closure, not on the row rule. 10p refilled after the 7h/8g region collapsed. Its neighbours did not settle, so treat it as an artefact until checked. AMBER
Gold, silver and the Planck scale
Gold (79) and silver (47) are both a full d shell plus one s electron. In this run the matching atoms would be 211, 283 and 355 (a full d shell, then one s electron). They are not 218 or 362, so the electrum label has no number behind it yet. One real coincidence: 47 + 79 = 126, which is a closed-shell number for nuclei. AMBER
Z size of the innermost electron cloud powers of ten above the Planck length 168 4.72e-13 m 22.5 218 3.64e-13 m 22.4 290 2.74e-13 m 22.2 362 2.19e-13 m 22.1
Even the most crushed-in electron in the heaviest atom is about 22 powers of ten bigger than the Planck length. Nothing in an atom gets to 1% under Planck. DEAD
For the smallest reader. We kept adding beads up to 366. The atom's coat buttoned up at 218, 290 and 362, just where the counting rule said. The golden ruler guessed wrong at 218 and 362, but the coats buttoned anyway. And even the tightest bead is still enormous next to the tiniest length there is.
Record
method as v0, grid 4000 pts to 100 bohr, l up to 6 (i), up to 13 levels per l
atoms 169–366 (198), unconverged 114 (convergence above 1e-4)
p-shell closures 218, 290, 330, 362
limit non-relativistic; ignores the dive at Z≈170; nuclei this heavy are not computed