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Chapter 6: Problem 72

Identify the group of elements that corresponds to each of the following generalized electron configurations: (a) [noble gas] \(n s^{2} n p^{5}\) (b) [noble gas] \(n s^{2}(n-1) d^{2}\) (c) [noble gas] \(n s^{2}(n-1) d^{10} n p^{1}\) (d) [noble gas] \(n s^{2}(n-2) f^{6}\)

Short Answer

Expert verified
(a) Group 17: Halogens (b) Group 4: Transition metals (c) Group 13 (d) Lanthanides and Actinides: Inner transition metals (f-block)

Step by step solution

01

(a) Identify the group for [noble gas] \(ns^2np^5\)

The elements with this electron configuration have two electrons in an s-orbital and five electrons in a p-orbital. The total number of valence electrons is 7. When we locate an element with 7 valence electrons in the periodic table, we find that they belong to Group 17, known as the halogens.
02

(b) Identify the group for [noble gas] \(ns^2(n-1)d^2\)

The elements with this electron configuration have two electrons in an s-orbital and two electrons in a d-orbital, which is one shell lower than their current outermost shell. The total number of valence electrons is 4. When we look for elements with 4 valence electrons in the periodic table, we find that they belong to Group 4 (transition metals).
03

(c) Identify the group for [noble gas] \(ns^2(n-1)d^{10}np^1\)

The elements with this electron configuration have two electrons in an s-orbital, a full d-orbital at the previous energy level, and one electron in a p-orbital. The total number of valence electrons is 3. When we search for elements with 3 valence electrons in the periodic table, we find that they belong to Group 13.
04

(d) Identify the group for [noble gas] \(ns^2(n-2)f^6\)

The elements with this electron configuration have two electrons in an s-orbital and six electrons in an f-orbital, which is two shells lower than their current outermost shell. These elements are part of the f-block, also known as the inner transition metals. Specifically, they belong to the lanthanides and actinides, which do not have a designated group number in the periodic table.

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Most popular questions from this chapter

(a) In terms of the Bohr theory of the hydrogen atom, what process is occurring when excited hydrogen atoms emit radiant energy of certain wavelengths and only those wavelengths? (b) Does a hydrogen atom "expand" or "contract" as it moves from its ground state to an excited state?

For each element, count the number of valence electrons, core electrons, and unpaired electrons in the ground state: (a) carbon, (b) phosphorus, (c) neon.

In the transition metals (the \(d\) -block), the electron configuration of cations is different than what you might expect. Instead of the \(\mathrm{d}\) electrons being lost first, \(s\) electrons are lost first. For example, the electron configuration of iron, \(\mathrm{Fe}\), is \([\mathrm{Ar}] 4 \mathrm{~s}^{2} 3 d^{6} ;\) but the electron configuration of \(\mathrm{Fe}^{2+}\) is \([\mathrm{Ar}] 3 d^{6} ;\) the \(4 \mathrm{~s}\) electrons are eliminated to make the cation. Write out the electron configurations of (a) \(\mathrm{Zn}^{2+}\) (b) \(\mathrm{Pt}^{2+}\) (c) \(\mathrm{Cr}^{3+}\) (d) \(\mathrm{Ti}^{4+}\).

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 a velocity of \(8.85 \times 10^{5} \mathrm{~cm} / \mathrm{s}\).

(a) According to the Bohr model, an electron in the ground state of a hydrogen atom orbits the nucleus at a specific radius of \(0.53 \AA\). In the quantum mechanical description of the hydrogen atom, the most probable distance of the electron from the nucleus is \(0.53 \AA\). Why are these two statements different? (b) Why is the use of Schr枚dinger's wave equation to describe the location of a particle very different from the description obtained from classical physics? (c) In the quantum mechanical description of an electron, what is the physical significance of the square of the wave function, \(\psi^{2} ?\)
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