Please help with both parts of the question. Thank you in advance! The number of electrons that each energy level n can hold is set by the possible quantum numbers and the Pauli Exclusion Principle. Sinceonly 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 manypossible 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 mi0,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 = 0when 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 eachenergy level. This pattern can be represented by a simple formula which can be used to quickly tell the number of electrons that a given shellcan hold. The formula is 2*n?How many electrons can the n = 4 shell hold?

Answered: Image /qna-images/answer/6202b174-f729-44cc-bdca-fb25072db75e.jpg

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?

3rd Edition

ISBN:9781111794378

Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Chapter8: Quantum Mechanics In Three Dimensions

Section: Chapter Questions

Problem 20P