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Chapter 7: Problem 154

Although no currently known elements contain electrons in g orbitals in the ground state, it is possible that these elements will be found or that electrons in excited states of known elements could be in \(g\) orbitals. For \(g\) orbitals, the value of \(\ell\) is \(4 .\) What is the lowest value of \(n\) for which \(g\) orbitals could exist? What are the possible values of \(m_{\ell} ?\) How many electrons could a set of \(g\) orbitals hold?

Short Answer

Expert verified
The lowest value of \(n\) for which \(g\) orbitals could exist is \(n = 5\). The possible values of \(m_{ℓ}\) are -4, -3, -2, -1, 0, 1, 2, 3, and 4. A set of \(g\) orbitals can hold a total of 18 electrons.

Step by step solution

01

Determine the quantum number relations

For g orbitals, the value of the azimuthal quantum number ℓ is given as 4. The relationship between the principal quantum number n and azimuthal quantum number ℓ is given by: n > ℓ where n is an integer greater than 0. Since ℓ = 4 for g orbitals, the lowest value of n that satisfies the relation above would be n = 5.
02

Finding the possible values of the magnetic quantum number

The magnetic quantum number m_ℓ can have values ranging from -ℓ to +ℓ, including zero. Therefore, for ℓ = 4, the possible values for m_ℓ are: m_ℓ = -4, -3, -2, -1, 0, 1, 2, 3, 4
03

Determine the number of electrons a set of g orbitals can hold

Each orbital can hold a maximum of two electrons, and the total number of orbitals for a given azimuthal quantum number ℓ is given by 2ℓ + 1. So, for g orbitals with ℓ = 4: Number of orbitals = 2(4) + 1 = 9 As each orbital can hold 2 electrons, the total number of electrons a set of g orbitals can hold is: Number of electrons = 9 orbitals * 2 electrons/orbital = 18 electrons

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Most popular questions from this chapter

Using the Heisenberg uncertainty principle, calculate \(\Delta x\) for each of the following. a. an electron with \(\Delta v=0.100 \mathrm{m} / \mathrm{s}\) b. a baseball (mass \(=145 \mathrm{g} )\) with $\Delta v=0.100 \mathrm{m} / \mathrm{s}$ c. How does the answer in part a compare with the size of a hydrogen atom? d. How does the answer in part b correspond to the size of a baseball?

In the ground state of element 115, Uup, a. how many electrons have \(n=5\) as one of their quantum numbers? b. how many electrons have \(\ell=3\) as one of their quantum numbers? c. how many electrons have \(m_{\ell}=1\) as one of their quantum numbers? d. how many electrons have \(m_{s}=-\frac{1}{2}\) as one of their quantum numbers?

How many valence electrons do each of the following elements have, and what are the specific valence electrons for each element? a. Ca b. O c. element 117 d. In e. Ar f. Bi

For each of the following pairs of elements $$(\mathrm{C} \text { and } \mathrm{N}) \quad(\text { Ar and Br })$$ pick the atom with a. more favorable (exothermic) electron affinity. b. higher ionization energy. c. larger size.

Write the expected ground-state electron configuration for the following: a. the element with one unpaired 5\(p\) electron that forms a covalent with compound fluorine b. the (as yet undiscovered) alkaline earth metal after radium c. the noble gas with electrons occupying 4f orbitals d. the first-row transition metal with the most unpaired electrons
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