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Chapter 6: Problem 77

Identify the specific element that corresponds to each of the following electron configurations and indicate the number of unpaired electrons for each: (a) \(1 s^{2} 2 s^{2}\), (b) \(1 s^{2} 2 s^{2} 2 p^{4}\), (c) \([\mathrm{Ar}] 4 s^{1} 3 d^{5}\), (d) \([\mathrm{Kr}] 5 s^{2} 4 d^{10} 5 p^{4}\).

Short Answer

Expert verified
(a) Element: Beryllium (Be), Unpaired Electrons: 0 (b) Element: Neon (Ne), Unpaired Electrons: 2 (c) Element: Chromium (Cr), Unpaired Electrons: 6 (d) Element: Tellurium (Te), Unpaired Electrons: 2

Step by step solution

01

(a) Identify Element and Unpaired Electrons for \(1s^2 2s^2\)

The electron configuration \(1s^2 2s^2\) belongs to an element with the last electron being in the 2s orbital. By filling in the principle quantum number and their electron capacity, the element with this configuration has 4 electrons. Thus, the element corresponds to the atomic number 4, which is beryllium (Be). Since there are no partially-filled orbitals, there are no unpaired electrons in this case. So, in the case of (a): Element = Be, Unpaired Electrons = 0.
02

(b) Identify Element and Unpaired Electrons for \(1s^2 2s^2 2p^4\)

The electron configuration \(1s^2 2s^2 2p^4\) belongs to an element with the last electron being in the 2p orbital. Filling in the principle quantum number and their electron capacity, the element with this configuration has 10 electrons. Thus, the element corresponds to the atomic number 10, which is neon (Ne). As for unpaired electrons, 2p^4 means that two 2p orbitals contain 2 electrons (paired) and one 2p orbital contains 2 unpaired electrons. So, in the case of (b): Element = Ne, Unpaired Electrons = 2.
03

(c) Identify Element and Unpaired Electrons for \([\mathrm{Ar}] 4s^1 3d^5\)

The electron configuration \([\mathrm{Ar}]4s^1 3d^5\) shows an element with Argon (\(\mathrm{Ar}\)) as its core and the last electron being in the 3d orbital. Argon corresponds to the atomic number 18. With one electron in the 4s orbital and five in the 3d orbitals, the total number of electrons for this element is 18 + 1 + 5 = 24, which corresponds to the element chromium (Cr). For unpaired electrons, 4s^1 and 3d^5 both have unpaired electrons, with a total of 1 + 5 = 6 unpaired electrons. In this case (c): Element = Cr, Unpaired Electrons = 6.
04

(d) Identify Element and Unpaired Electrons for \([\mathrm{Kr}] 5s^2 4d^{10} 5p^4\)

The electron configuration \([\mathrm{Kr}] 5s^2 4d^{10} 5p^4\) contains the core krypton (\(\mathrm{Kr}\)), with the last electron being in the 5p orbital. Krypton corresponds to the atomic number 36. The number of electrons for this element is 36 + 2 + 10 + 4 = 52, which corresponds to the element tellurium (Te). For unpaired electrons, we have 5p^4, which means two 5p orbitals contain 2 electrons (paired) and one 5p orbital contains 2 unpaired electrons, for a total of 2 unpaired electrons. So, in the case of (d): Element = Te, Unpaired Electrons = 2.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Atomic Number
An atomic number is a fundamental property of an element on the periodic table. It represents the number of protons found in the nucleus of an atom, and thus defines the element itself. For example, if an atom has an atomic number of 2, it means it has two protons and corresponds to helium.

  • The atomic number directly influences the element's position in the periodic table.
  • It is often used to determine electronic configurations, as each electron in a neutral atom balances the positive charge of a proton.
  • For an atom, determining the atomic number also helps in identifying the element. For instance, if an element has an atomic number of 6, it is carbon.

Knowing the atomic number is essential for solving problems related to electron configurations because it helps us navigate through the periodic table and identify which element corresponds to a specific electron arrangement.
Unpaired Electrons
Unpaired electrons play a significant role in the chemical behavior of atoms, particularly in their magnetic and chemical properties. An electron is considered unpaired if it occupies an orbital alone, without a partner electron of opposite spin.

  • Atoms with unpaired electrons are generally more reactive than those whose electrons are all paired.
  • Unpaired electrons contribute to the paramagnetic nature of substances, meaning they tend to be attracted by magnetic fields.
  • The number of unpaired electrons is found by examining an atom's electron configuration, particularly the distribution in their outermost orbitals.

For example, if a configuration ends with \(2p^4\), two of the 2p orbitals will contain paired electrons, and one will have two unpaired electrons. Such knowledge aids in predicting the bonding nature and reactivity of elements.
Periodic Table Elements
The periodic table is a systematic arrangement of elements based on their atomic number, electron configuration, and recurring chemical properties. It is an essential tool in understanding how different elements relate to each other.

  • Elements are organized into periods (rows) and groups (columns), the latter of which share similar chemical properties.
  • The table differentiates elements into groups such as alkali metals, transition metals, noble gases, etc.
  • Knowing an element's position helps determine its electron configuration, which directly affects its chemical behavior.

Using the periodic table, one can easily trace the electron configurations by moving across periods and following groups, thereby identifying elements efficiently. Recognizing these patterns is key for anyone studying chemistry, as it simplifies understanding complex concepts such as bonding, reactivity, and the arrangement of electrons in atoms.

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

(a) Consider the following three statements: (i) A hydrogen atom in the \(n=3\) state can emit light at only two specific wavelengths, (ii) a hydrogen atom in the \(n=2\) state is at a lower energy than the \(n=1\) state, and (iii) the energy of an emitted photon equals the energy difference of the two states involved in the emission. Which of these statements is or are true? (b) Does a hydrogen atom "expand" or "contract" as it moves from its ground state to an excited state?

Titanium metal requires a photon with a minimum energy of $6.94 \times 10^{-19} \mathrm{J}$ to emit electrons. (a) What is the minimum frequency of light necessary to emit electrons from titanium via the photoelectric effect? (b) What is the wavelength of this light? (c) Is it possible to eject electrons from titanium via the photoelectric effect? (b) What is the wavelength of this light? (c) Is it possible to eject electrons from titanium metal using visible light? (d) If titanium is irradiated with light of wavelength \(233 \mathrm{nm},\) what is the madimum possible kinetic energy of the emitted electrons?

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 .

(a) What are "valence electrons"? (b) What are "core electrons"? (c) What does each box in an orbital diagram represent? (d) What quantity is represented by the half arrows in an orbital diagram?
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