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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
For the 2p subshell: \(n = 2\), \(l = 1\), and \(m_l\) values are -1, 0, and +1. There are three orbitals with quantum numbers (2, 1, -1), (2, 1, 0), and (2, 1, +1). For the 5d subshell: \(n = 5\), \(l = 2\), and \(m_l\) values are -2, -1, 0, +1, and +2. There are five orbitals with quantum numbers (5, 2, -2), (5, 2, -1), (5, 2, 0), (5, 2, +1), and (5, 2, +2).

Step by step solution

01

Identify the values of n and l

In the 2p subshell, the principal quantum number n is 2 (it comes directly from the number in subshell notation), and the azimuthal quantum number l is associated with the letter p. The values of l are as follows: \(s = 0, p = 1, d = 2, f = 3, ... \) In this case, l = 1 because we are dealing with the p subshell.
02

Identify the values of ml for the p subshell

For the p subshell (l = 1), the magnetic quantum number ml can take values from -l to +l, with a step of 1, including 0. So for a p subshell (l = 1), ml can be -1, 0, or +1.
03

Write the values of n, l, and ml for each orbital in the 2p subshell

The 2p subshell has three orbitals, which can be represented by the quantum numbers: (a) n = 2, l = 1, ml = -1 (b) n = 2, l = 1, ml = 0 (c) n = 2, l = 1, ml = +1 For the 5d subshell:
04

Identify the values of n and l

In the 5d subshell, the principal quantum number n is 5, and the azimuthal quantum number l corresponds to the letter d. As stated earlier, for the d subshell, l = 2.
05

Identify the values of ml for the d subshell

For the d subshell (l = 2), the magnetic quantum number ml can take values from -l to +l, with a step of 1. So for a d subshell (l = 2), ml can be -2, -1, 0, +1, or +2.
06

Write the values of n, l, and ml for each orbital in the 5d subshell

The 5d subshell has five orbitals, which can be represented by the quantum numbers: (a) n = 5, l = 2, ml = -2 (b) n = 5, l = 2, ml = -1 (c) n = 5, l = 2, ml = 0 (d) n = 5, l = 2, ml = +1 (e) n = 5, l = 2, ml = +2

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Most popular questions from this chapter

Among the elementary subatomic particles of physics is the muon, which decays within a few nanoseconds after formation. The muon has a rest mass \(206.8\) times that of an electron. Calculate the de Broglie wavelength associated with a muon traveling at \(8.85 \times 10^{5} \mathrm{~cm} / \mathrm{s}\).

The Lyman series of emission lines of the hydrogen atom are those for which \(n_{\mathrm{f}}=1\). (a) Determine the region of the electromagnetic spectrum in which the lines of the Lyman series are observed. (b) Calculate the wavelengths of the first three lines in the Lyman series-those for which \(n_{\mathrm{i}}=2,3\), and 4 .

The familiar phenomenon of a rainbow results from the diffraction of sunlight through raindrops. (a) Does the wavelength of light increase or decrease as we proceed outward from the innermost band of the rainbow? (b) Does the frequency of light increase or decrease as we proceed outward? (c) Suppose that instead of sunlight, the visible light from a hydrogen discharge tube (Figure 6.10) was used as the light source. What do you think the resulting "hydrogen discharge rainbow" would look like? [Section 6.3]

(a) What are the similarities of and differences between the \(1 \mathrm{~s}\) and \(2 s\) orbitals of the hydrogen atom? (b) In what sense does a \(2 p\) orbital have directional character? Compare the "directional" characteristics of the \(p_{x}\) and \(d_{x^{2}-y^{2}}\) orbitals. (That is, in what direction or region of space is the electron density concentrated?) (c) What can you say about the average distance from the nucleus of an electron in a \(2 s\) orbital as compared with a \(3 s\) orbital? (d) For the hydrogen atom, list the following orbitals in order of increasing energy (that is, most stable ones first): \(4 f, 6 s, 3 d, 1 s, 2 p\).

State where in the periodic table these elements appear: (a) elements with the valence-shell electron configuration \(n s^{2} n p^{5}\) (b) elements that have three unpaired \(p\) electrons (c) an element whose valence electrons are \(4 s^{2} 4 p^{1}\) (d) the \(d\)-block elements [Section 6.9]
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