Atom Calculator — Protons, Neutrons, Electrons & Binding Energy
Enter the atomic number (Z) and mass number (A) of any nucleus — plus the ion charge if it's not a neutral atom — and instantly see proton, neutron and electron counts, the neutron-to-proton ratio, and the nuclear binding energy estimated from the Bethe-Weizsäcker semi-empirical formula.
Ion charge
Semi-empirical Bethe-Weizsäcker estimate; real value differs slightly for light nuclei
- 1
Volume term a_V × A
15,75 × 12 = 189 - 2
Surface term a_S × A^⅔
17,8 × 12^⅔ = 93,3 - 3
Coulomb term a_C × Z(Z−1) ÷ A^⅓
0,711 × 6 × 5 ÷ 12^⅓ = 9,32 - 4
Asymmetry term a_A × (A−2Z)² ÷ A
23,7 × (12 − 2×6)² ÷ 12 = 0 - 5
Pairing term ±a_P ÷ √A
3,23Even-even nucleus: positive pairing bonus. - 6
Binding energy vol − surf − coul − asym + pair
189 − 93,3 − 9,32 − 0 + (3,23) = 89,6
Kako deluje ta kalkulator?
An atom has Z protons, A−Z neutrons, and Z electrons (adjusted by charge for ions). Nuclear binding energy is estimated via the Bethe-Weizsäcker formula: BE ≈ a_V·A − a_S·A^⅔ − a_C·Z(Z−1)/A^⅓ − a_A·(A−2Z)²/A ± pairing. Peak stability (~8.7 MeV/nucleon) occurs near iron-56.
Formula
How this is calculated
An atom consists of a nucleus of protons (atomic number Z) and neutrons (neutron number N = A − Z), surrounded by electrons equal in number to the protons for a neutral atom. For an ion with charge +q, q electrons have been removed, leaving Z − q electrons. The mass number A is simply the total count of nucleons (protons + neutrons).
The nuclear binding energy — the energy that holds the nucleus together — is estimated using the Bethe-Weizsäcker semi-empirical mass formula, developed in 1935–1936. It models the nucleus like a liquid drop with five terms: a volume term (proportional to A, bulk binding), a surface term (surface nucleons have fewer neighbours), a Coulomb term (proton-proton repulsion), an asymmetry term (penalises nuclei where Z ≠ N), and a pairing term (even-even nuclei are extra stable). The constants used here are: a_V = 15.75, a_S = 17.80, a_C = 0.711, a_A = 23.70, δ = ±11.18/√A MeV.
The formula is highly accurate for medium to heavy nuclei (A ≳ 20) but becomes less reliable for very light nuclei like helium or lithium, where quantum shell effects dominate. The peak binding energy per nucleon (~8.7 MeV) occurs near iron-56, which is why stellar nucleosynthesis stalls there.
Pogosta vprašanja
Subtract the atomic number (Z, protons) from the mass number (A, protons + neutrons): N = A − Z. For carbon-12, Z = 6 and A = 12, so N = 6 neutrons.
Binding energy is the energy required to completely disassemble a nucleus into its individual protons and neutrons. A higher binding energy per nucleon means a more stable nucleus. Iron-56 has one of the highest binding energies per nucleon of any element.
The formula treats the nucleus as a classical liquid drop, averaging over quantum effects. Real binding energies deviate from the prediction at "magic numbers" (2, 8, 20, 28, 50, 82 nucleons) where shell closures provide extra stability — the same reason noble gas atoms are chemically inert.
Znano tudi kot
TG we-Calculate Editorial Team. (2026). Atom Calculator — Protons, Neutrons, Electrons & Binding Energy [Online calculator]. TG we-Calculate. https://we-calculate.com/sl/calculator/atom-calculator
TG we-Calculate Editorial Team. "Atom Calculator — Protons, Neutrons, Electrons & Binding Energy." TG we-Calculate. 2026. https://we-calculate.com/sl/calculator/atom-calculator.
TG we-Calculate Editorial Team, "Atom Calculator — Protons, Neutrons, Electrons & Binding Energy," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/sl/calculator/atom-calculator
@misc{wecalculate_atom_calculator, title = {Atom Calculator — Protons, Neutrons, Electrons & Binding Energy}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/sl/calculator/atom-calculator}}, year = {2026}, note = {TG we-Calculate} }
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