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Chapter 6: Problem 58

Give the values for \(n, l,\) and \(m_{l}\) for (a) each orbital in the 2\(p\) subshell, (b) each orbital in the 5\(d\) subshell.

Short Answer

Expert verified
(a) For the 2p subshell: \(n = 2\), \(l = 1\), and \(m_l\) values are -1, 0, and +1. (b) For the 5d subshell: \(n = 5\), \(l = 2\), and \(m_l\) values are -2, -1, 0, +1, and +2.

Step by step solution

01

Find the azimuthal quantum number (l) for the p subshell

The azimuthal quantum number (l) is 0 for the s subshell, 1 for the p subshell, 2 for the d subshell, and so on. Therefore, for the p subshell, l = 1.
02

Find the magnetic quantum number (m_l) values for the 2p subshell

Knowing that l = 1, the magnetic quantum numbers (m_l) can take values from -l to +l. Therefore, in the 2p subshell, m_l can have the values -1, 0, +1. There are three possible orbitals in the 2p subshell. So, for the 2p subshell, we have: - n = 2 - l = 1 - m_l: -1, 0, +1 (b) The 5d subshell: As given, the energy level (n) is 5, and the subshell is d. So, our task here is to find the value of l for the d subshell and the values of m_l for each orbital in the 5d subshell.
03

Find the azimuthal quantum number (l) for the d subshell

For the d subshell, l = 2.
04

Find the magnetic quantum number (m_l) values for the 5d subshell

Knowing that l = 2, the magnetic quantum numbers (m_l) can take values from -l to +l. Therefore, in the 5d subshell, m_l can have the values -2, -1, 0, +1, +2. There are five possible orbitals in the 5d subshell. So, for the 5d subshell, we have: - n = 5 - l = 2 - m_l: -2, -1, 0, +1, +2

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