The number of electrons that each energy level n can hold is set by the possible quantum numbers and the Pauli Exclusion Principle. Since only one electron can occupy a given quantum state, you can only have as many electrons as quantum states (n, I, mı, m, combinations). Because m, can always be 1/2 (spin up) or -1/2 (spin down) regardless of the n, I, m¡ combination, all you need to do is to find how many possible I, m, combinations exist for a given n and multiply by 2 in order to find the total number of states for a given n. For n = 1: | = 0 and m = 0, thus at the first shell (ground state) you can only have 1 1, m, combination, or 2*(1) electrons. For n = 2: | = 0, 1 (0 or 1) when I = 0: m = 0 when I = 1: m, = -1, 0, 1 (-1 or O or 1), thus at the second shell you can have 3+1 I, m¡ combinations, or 2*(4) electrons. How many electrons can you have on the 3rd shell (n = 3)? Hopefully by working out the answer of the previous question you realized that there is a pattern for the number of allowed states at each energy level. This pattern can be represented by a simple formula which can be used to quickly tell the number of electrons that a given shell can hold. The formula is 2*n? How many electrons can the n = 4 shell hold?
The number of electrons that each energy level n can hold is set by the possible quantum numbers and the Pauli Exclusion Principle. Since only one electron can occupy a given quantum state, you can only have as many electrons as quantum states (n, I, mı, m, combinations). Because m, can always be 1/2 (spin up) or -1/2 (spin down) regardless of the n, I, m¡ combination, all you need to do is to find how many possible I, m, combinations exist for a given n and multiply by 2 in order to find the total number of states for a given n. For n = 1: | = 0 and m = 0, thus at the first shell (ground state) you can only have 1 1, m, combination, or 2*(1) electrons. For n = 2: | = 0, 1 (0 or 1) when I = 0: m = 0 when I = 1: m, = -1, 0, 1 (-1 or O or 1), thus at the second shell you can have 3+1 I, m¡ combinations, or 2*(4) electrons. How many electrons can you have on the 3rd shell (n = 3)? Hopefully by working out the answer of the previous question you realized that there is a pattern for the number of allowed states at each energy level. This pattern can be represented by a simple formula which can be used to quickly tell the number of electrons that a given shell can hold. The formula is 2*n? How many electrons can the n = 4 shell hold?
College Physics
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Transcribed Image Text:The number of electrons that each energy level n can hold is set by the possible quantum numbers and the Pauli Exclusion Principle. Since
only one electron can occupy a given quantum state, you can only have as many electrons as quantum states (n, I, m, m, combinations).
Because m, can always be 1/2 (spin up) or -1/2 (spin down) regardless of the n, I, mj combination, all you need to do is to find how many
possible I, m, combinations exist for a given n and multiply by 2 in order to find the total number of states for a given n.
For n = 1:
| = 0 and mi
0,
thus at the first shell (ground state) you can only have 1 1, m, combination, or 2*(1) electrons.
For n = 2:
| = 0, 1 (0 or 1)
when I = 0: m = 0
when I = 1: m, = -1, 0, 1 (-1 or 0 or 1),
thus at the second shell you can have 3+1 I, m combinations, or 2*(4) electrons.
How many electrons can you have on the 3rd shell (n = 3)?
Hopefully by working out the answer of the previous question you realized that there is a pattern for the number of allowed states at each
energy level. This pattern can be represented by a simple formula which can be used to quickly tell the number of electrons that a given shell
can hold. The formula is 2*n?
How many electrons can the n = 4 shell hold?
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