Same distance of electrons from the nucleus for same element

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SUMMARY

The distance of electrons from the nucleus in the same element is not a fixed quantity but is determined by the electron's wavefunction, which varies based on the state of the atom. The most probable distance to find an electron is state-dependent and governed by the Schrödinger equation. Identical elements will exhibit the same electron distance only when they are in the exact same quantum state. Therefore, the concept of distance in atomic physics is contextually tied to the electron's energy state and wavefunction characteristics.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with wavefunctions and their significance in atomic physics
  • Knowledge of the Schrödinger equation and its applications
  • Basic concepts of atomic states and eigenstates
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  • Study the implications of the Schrödinger equation in quantum mechanics
  • Explore the concept of wavefunctions and their role in electron positioning
  • Investigate the differences between quantum states of identical elements
  • Learn about the probabilistic interpretation of quantum mechanics
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Students and professionals in physics, particularly those focused on quantum mechanics, atomic theory, and anyone interested in the behavior of electrons in atoms.

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Why distance of electrons from the nucleus is the same for same element?
 
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In atomic scale physicists normally do not talk about "distance" unless in practical context. Electron's presence around the nucleus is described by its wavefunction which is a function of space. By distance, you must mean the most probable distance to find an electron in a particular state from the nucleus. This quantity is state/wavefunction dependent, and what determines the eigenstate of an atom is its associated Schroedinger equation. The most probable distance to find an electron need not necessarily the same for same element, again it depends on the state of that atomic element at that instant of time. only when two identical elements are exactly in the same state, will you find the electron's most probable position exactly the same.
 

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