About

Miscounting electrons or misidentifying orbital filling order leads to incorrect Lewis structures, wrong bond angles, and failed reaction predictions. The Aufbau principle dictates filling order by n + l rule, but 20 elements deviate from it. Chromium adopts [Ar] 3d⁵ 4s¹ instead of the predicted 3d⁴ 4s² due to half-filled subshell stability. This tool implements the complete Madelung energy ordering with all known exceptions hardcoded from NIST data for elements Z = 1 through 118.

Beyond configuration, the calculator determines isotope neutron count (N = A − Z), mass-energy equivalence via E = mc², molar quantities, and renders an interactive Bohr model. Note: electron configurations for superheavy elements (Z > 108) are theoretical predictions and may be revised as experimental data becomes available.

Formulas

The number of neutrons in a specific isotope is the difference between its mass number and atomic number:

N = A − Z

where N = neutron count, A = mass number (total nucleons), Z = atomic number (proton count).

Mass-energy equivalence converts rest mass to energy:

E = mc²

where E = energy in J, m = mass in kg, c = 2.998 × 10⁸ m/s (speed of light in vacuum).

The number of atoms in a given mass of a pure element:

n_atoms = mM × N_A

where m = sample mass in g, M = molar mass in g/mol, N_A = 6.022 × 10²³ mol⁻¹ (Avogadro constant).

Electron filling order follows the Madelung rule: orbitals fill in order of increasing n + l, and for equal sums, the lower n fills first. The sequence is: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p.

Reference Data

Z	Symbol	Name	Mass (u)	Electron Config.	Electronegativity	Category
1	H	Hydrogen	1.008	1s¹	2.20	Nonmetal
2	He	Helium	4.003	1s²	-	Noble gas
3	Li	Lithium	6.941	[He] 2s¹	0.98	Alkali metal
6	C	Carbon	12.011	[He] 2s² 2p²	2.55	Nonmetal
7	N	Nitrogen	14.007	[He] 2s² 2p³	3.04	Nonmetal
8	O	Oxygen	15.999	[He] 2s² 2p⁴	3.44	Nonmetal
11	Na	Sodium	22.990	[Ne] 3s¹	0.93	Alkali metal
14	Si	Silicon	28.086	[Ne] 3s² 3p²	1.90	Metalloid
17	Cl	Chlorine	35.453	[Ne] 3s² 3p⁵	3.16	Halogen
20	Ca	Calcium	40.078	[Ar] 4s²	1.00	Alkaline earth
24	Cr	Chromium	51.996	[Ar] 3d⁵ 4s¹	1.66	Transition metal
26	Fe	Iron	55.845	[Ar] 3d⁶ 4s²	1.83	Transition metal
29	Cu	Copper	63.546	[Ar] 3d¹⁰ 4s¹	1.90	Transition metal
47	Ag	Silver	107.868	[Kr] 4d¹⁰ 5s¹	1.93	Transition metal
55	Cs	Cesium	132.905	[Xe] 6s¹	0.79	Alkali metal
74	W	Tungsten	183.840	[Xe] 4f¹⁴ 5d⁴ 6s²	2.36	Transition metal
79	Au	Gold	196.967	[Xe] 4f¹⁴ 5d¹⁰ 6s¹	2.54	Transition metal
82	Pb	Lead	207.200	[Xe] 4f¹⁴ 5d¹⁰ 6s² 6p²	1.87	Post-trans. metal
86	Rn	Radon	222.000	[Xe] 4f¹⁴ 5d¹⁰ 6s² 6p⁶	2.20	Noble gas
92	U	Uranium	238.029	[Rn] 5f³ 6d¹ 7s²	1.38	Actinide
94	Pu	Plutonium	244.000	[Rn] 5f⁶ 7s²	1.28	Actinide
118	Og	Oganesson	294.000	[Rn] 5f¹⁴ 6d¹⁰ 7s² 7p⁶	-	Noble gas (pred.)

Frequently Asked Questions

Half-filled and fully-filled subshells possess extra stability due to exchange energy. In Chromium (Z = 24), promoting one 4s electron into 3d yields five unpaired d-electrons, maximizing exchange energy. The energy gain from this symmetric half-filled 3d⁵ configuration outweighs the cost of depopulating 4s. Similar exceptions occur for Cu (Z = 29), Ag (Z = 47), Au (Z = 79), and several others. This calculator hardcodes all NIST-recognized exceptions.

Chemical properties depend almost entirely on electron count (equal to Z for neutral atoms), not mass number A. Isotopes of the same element share identical electron configurations and nearly identical bonding behavior. However, A determines nuclear stability, decay modes, and binding energy per nucleon. For very light elements (e.g., Hydrogen vs. Deuterium), the mass difference is proportionally large enough to cause measurable kinetic isotope effects in reaction rates.

The energy E = mc² represents the total rest energy stored in a mass. For a single atom of 23592U, the rest energy is approximately 3.54 × 10⁻⁸ J. In fission, only about 0.09% of this rest mass converts to kinetic energy (~200 MeV per fission event). The calculator shows total rest energy, which is the theoretical upper bound.

Configurations for superheavy elements (Z > 108) are predictions based on relativistic Dirac-Fock calculations. Relativistic effects (electrons traveling at significant fractions of c) cause s and p orbital contraction and d/f orbital expansion, potentially altering the filling order. Experimental confirmation exists only for a few fleeting atoms. Treat configurations for Z ≥ 104 as best theoretical estimates.

The Bohr model depicts electrons in fixed circular orbits at discrete radii. Quantum mechanics replaces orbits with probability clouds (orbitals) described by wavefunctions. The Bohr model correctly predicts shell capacities (2n²) and energy levels for hydrogen-like atoms, but fails for multi-electron systems. The visualization here serves as a pedagogical tool showing shell occupancy, not spatial distribution. For accurate probability densities, consult Hartree-Fock or DFT orbital plots.

For main group elements, valence electrons occupy the outermost shell (highest n). For transition metals, both the outermost s-electrons and the partially filled (n−1)d electrons participate in bonding. Iron ([Ar] 3d⁶ 4s²) has 2 s-valence electrons but can utilize up to 8 electrons (3d + 4s) in bonding, explaining its multiple oxidation states (+2 and +3 most common). This calculator reports the outer-shell s and p electrons as the primary valence count.