Question about electrons per shell

In summary, the maximum number of electrons per shell is determined by the degeneracy of the energy shell and the Pauli exclusion principle. The number of orbitals in each shell is determined by the possible angular momentum states for the electrons, as predicted by the Schrödinger Equation. While a pattern of 2,8,16,32,50 may seem more mathematically pleasing, it does not align with the predictions of the Schrödinger Equation. Splitting an electron in half to fit 71.5 electrons in a shell is not possible due to the structure of the nucleus.
  • #1
nuby
336
0
why is it the maximum electrons per shell is 2,8,18,32,50 ... Wouldn't 2,8,16,32,50 make more sense mathematically?

Are there any equations the show why this occurs?
 
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  • #2
It is due, first due to the degeneracy of the energy shell (i.e. how many energy states that have that shell's energy) and also due to the pauli exclusion principle.

First, the higher energy shells have bigger degeneracies. In simple terms, there are more orbitals in the n=2 shell than there are in the n=1 energy shell. Thus, they can hold more electrons. Each orbital can hold a maximum of two electrons with opposite spin due to the Pauli principle. So the end result is:

n=1 Shell: 1 orbital = 2 electrons

n=2 Shell: 4 orbitals= 8 electrons

n=3 Shell: 9 orbitals= 18 electrons

The number of orbitals is determined by the number of possible angular momentum states for the electrons in the atom, which is predicted by the Schrödinger Equation. So, while your pattern may seem nicer or more aesthetic, it is not what the Schrödinger Equation predicts, so it does not make more sense mathematically in the end.
 
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  • #3
Is this possible? n=6
71.5 electrons?
 
  • #4
nuby said:
Is this possible? n=6
71.5 electrons?

That might be a bit difficult; splitting an electron in half is not something that you just do with a hammer and chisel...
 
  • #5
Lol. nevermind
 
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  • #6
nucleus

dont forget that the nucleus also has shells and subshells.
 

Related to Question about electrons per shell

1. What are electrons per shell?

Electrons per shell refers to the number of electrons that can occupy a specific energy level within an atom. The first energy level, or shell, can hold a maximum of 2 electrons, while the second and third levels can hold up to 8 electrons each. The number of electrons per shell increases as you move further away from the nucleus.

2. How are electrons distributed in different shells?

The electrons in an atom are distributed into different shells according to the Aufbau principle, which states that electrons fill the lowest energy levels first before moving to higher energy levels. This means that the first shell is filled before any electrons can occupy the second shell, and so on.

3. What determines the number of electrons per shell?

The number of electrons per shell is determined by the atomic number of an element. The atomic number is equal to the number of protons in an atom, which also determines the number of electrons. For example, carbon has an atomic number of 6, so it has 6 electrons, with 2 in the first shell and 4 in the second shell.

4. Can the number of electrons per shell change?

The number of electrons per shell can change if the atom undergoes a chemical reaction or gains or loses electrons. This can result in a change in the atom's overall charge and may lead to the formation of ions. However, the number of electrons that can occupy each shell remains the same.

5. What is the maximum number of electrons per shell?

The maximum number of electrons per shell is determined by the formula 2n^2, where n is the number of the shell. For example, the first shell can hold a maximum of 2 electrons (2 x 1^2 = 2), the second shell can hold a maximum of 8 electrons (2 x 2^2 = 8), and the third shell can hold a maximum of 18 electrons (2 x 3^2 = 18). This pattern continues for higher energy levels.

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