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Chapter 7: Problem 144

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 mℓ are -4, -3, -2, -1, 0, 1, 2, 3, and 4, and a set of g orbitals can hold 18 electrons.

Step by step solution

01

Finding the lowest value of n where a g orbital can exist

According to the quantum numbers, the relation between n and ℓ is that ℓ can take values from 0 to n-1. For g orbitals, ℓ = 4. So we need to find the smallest value of n for which this condition holds. n - 1 >= 4 n >= 5 So, the lowest value of n for which g orbitals could exist is n = 5.
02

Finding possible values of mℓ

The value of the magnetic quantum number mℓ ranges from -ℓ to ℓ in integer steps. Since we know that for g orbitals, ℓ = 4, we can now find the possible values of mℓ: -4, -3, -2, -1, 0, 1, 2, 3, 4
03

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

To find the number of electrons a set of g orbitals can hold, we have to consider that each orbital can hold two electrons with opposite spins. We have calculated 9 possible values for mℓ, which means there are 9 orbitals in the set of g orbitals. Hence, the total number of electrons that a set of g orbitals can hold is 9 orbitals * 2 electrons/orbital = 18 electrons. In conclusion, the lowest value of n for which g orbitals could exist is n = 5, the possible values of mℓ are -4, -3, -2, -1, 0, 1, 2, 3, and 4, and the number of electrons a set of g orbitals can hold is 18 electrons.

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Most popular questions from this chapter

An excited hydrogen atom emits light with a wavelength of \(397.2 \mathrm{~nm}\) to reach the energy level for which \(n=2\). In which principal quantum level did the electron begin?

Which of the following statements is(are) true? a. \(\mathrm{F}\) has a larger first ionization energy than does \(\mathrm{Li}\). b. Cations are larger than their parent atoms. c. The removal of the first electron from a lithium atom (electron configuration is \(1 s^{2} 2 s^{1}\) ) is exothermic - that is, removing this electron gives off energy. d. The He atom is larger than the \(\mathrm{H}^{+}\) ion. e. The \(\mathrm{Al}\) atom is smaller than the \(\mathrm{Li}\) atom.

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

An electron is excited from the \(n=1\) ground state to the \(n=3\) state in a hydrogen atom. Which of the following statements are true? Correct the false statements to make them true. a. It takes more energy to ionize (completely remove) the electron from \(n=3\) than from the ground state. b. The electron is farther from the nucleus on average in the \(n=3\) state than in the \(n=1\) state. c. The wavelength of light emitted if the electron drops from \(n=3\) to \(n=2\) will be shorter than the wavelength of light emitted if the electron falls from \(n=3\) to \(n=1\). d. The wavelength of light emitted when the electron returns to the ground state from \(n=3\) will be the same as the wavelength of light absorbed to go from \(n=1\) to \(n=3\). e. For \(n=3\), the electron is in the first excited state.

The bright yellow light emitted by a sodium vapor lamp consists of two emission lines at \(589.0\) and \(589.6 \mathrm{~nm}\). What are the frequency and the energy of a photon of light at each of these wavelengths? What are the energies in \(\mathrm{kJ} / \mathrm{mol}\) ?
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