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Chapter 7: Problem 55

Give the values of the quantum numbers associated with the following orbitals: (a) \(2 p,\) (b) \(3 s,\) (c) \(5 d\).

Short Answer

Expert verified
The Quantum numbers for \(2 p\) are \(n = 2, l = 1, m_l = -1, 0, 1, m_s = +½, -½\). For \(3 s\) are \(n = 3, l=0, m_l = 0, m_s = +½, -½\). And for \(5 d\), they are \(n=5, l=2, m_l = -2, -1, 0, 1, 2, m_s = +½, -½\).

Step by step solution

01

Identification of the quantum numbers for \(2 p\)

For a \(2 p\) orbital, quantum numbers are as following: Principal quantum number (\(n\)) is 2 as it denotes the main energy level of an electron in an atom. Azimuthal quantum number (\(l\)) i.e., the one indicates the shape of the electron's orbital is 1. This corresponds to \(p\) orbitals. Magnetic quantum number (\(m_l\)) varies between -\(l\) and \(l\). In this case, it can be -1, 0, or 1. The fourth quantum number called the Spin quantum number (\(m_s\)) can only be +½ or -½ that state the spin of an electron.
02

Identification of the quantum numbers for \(3 s\)

In a \(3 s\) orbital: Principal quantum number (\(n\)) is 3. Azimuthal quantum number (\(l\)) is 0, for \(s\) type orbital. The corresponding Magnetic quantum number (\(m_l\)) is 0 because the range of the \(m_l\) values is from -\(l\) to \(l\). The Spin quantum number (\(m_s\)) again, can be either +½ or -½.
03

Identification of the quantum numbers for \(5 d\)

For a \(5 d\) orbital, the quantum numbers are as follows: Principal quantum number (\(n\)) is 5. The Azimuthal quantum number (\(l\)) is 2 because 'd' type orbital corresponds to \(l=2\). For 'd' type orbitals the Magnetic quantum number (\(m_l\)) ranges from -2 to 2 hence it can have five possible values: -2, -1, 0, 1, or 2. The Spin quantum number (\(m_s\)) again can be either +½ or -½

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Most popular questions from this chapter

For each of the following pairs of hydrogen orbitals, indicate which is higher in energy: (a) \(1 s, 2 s ;\) (b) \(2 p\), \(3 p ;\) (c) \(3 d_{x y}, 3 d_{y z};\) (d) \(3 s, 3 d ;\) (e) 4f, \(5 s.\)

Which quantum number defines a shell? Which quantum numbers define a subshell?

When an electron makes a transition between energy levels of a hydrogen atom, there are no restrictions on the initial and final values of the principal quantum number \(n\). However, there is a quantum mechanical rule that restricts the initial and final values of the orbital angular momentum \(\ell\). This is the selection rule, which states that \(\Delta \ell=\pm 1,\) that is, in a transition, the value of \(\ell\) can only increase or decrease by one. According to this rule, which of the following transitions are allowed: (a) \(1 s \longrightarrow 2 s\), (b) \(2 p \longrightarrow 1 s\) (c) \(1 s \longrightarrow 3 d\) (d) \(3 d \longrightarrow 4 f\), (e) \(4 d \longrightarrow 3 s ?\)

Is it possible for a fluorescent material to emit radiation in the ultraviolet region after absorbing visible light? Explain your answer.

Write the ground-state electron configurations for the following elements: \(\mathrm{B}, \mathrm{V}, \mathrm{Ni}, \mathrm{As}, \mathrm{I}, \mathrm{Au}\).
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