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Chapter 6: Problem 74

The following electron configurations represent excited states. Identify the element, and write its ground-state condensed electron configuration. (a) \(\mathrm{ls}^{2} 2 s^{2} 3 p^{2} 4 p^{1}\), (b) \([\operatorname{Ar}] 3 d^{10} 4 s^{1} 4 p^{4} 5 s^{1}\), (c) \([\operatorname{Kr}] 4 d^{6} 5 s^{2} 5 p^{1}\).

Short Answer

Expert verified
The elements and their ground-state condensed electron configurations are: (a) Nitrogen (N): \(\mathrm{1s^{2} 2s^{2} 2p^{3}}\) (b) Selenium (Se): \([\operatorname{Ar}] 3 d^{10} 4 s^{2} 4 p^{4}\) (c) Rhodium (Rh): \([\operatorname{Kr}] 4d^{5} 5s^{1}\)

Step by step solution

01

Identify the elements

To identify the elements, find the total number of electrons in the excited configurations. (a)\(\mathrm{ls}^{2} 2 s^{2} 3 p^{2} 4 p^{1}\)\\ Total number of electrons = 2 + 2 + 2 +1 = 7, which is Nitrogen (N). (b) \([\operatorname{Ar}] 3 d^{10} 4 s^{1} 4 p^{4} 5 s^{1}\)\\ Argon has 18 electrons, so total number of electrons = 18 +10 +1 + 4+ 1 = 34, which is Selenium (Se). (c) \([\operatorname{Kr}] 4 d^{6} 5 s^{2} 5 p^{1}\)\\ Krypton has 36 electrons, so total number of electrons = 36+6 +2 + 1=45, which is Rhodium (Rh).
02

Write the ground-state condensed electron configurations

(a) Nitrogen (N), with 7 electrons, has the following ground-state configuration: \(\mathrm{1s^{2} 2s^{2} 2p^{3}}\). (b) Selenium (Se), with 34 electrons, has the following ground-state configuration: \([\operatorname{Ar}] 3 d^{10} 4 s^{2} 4 p^{4}\). (c) Rhodium (Rh), with 45 electrons, has the following ground-state configuration: \([\operatorname{Kr}] 4d^{5} 5s^{1}\).

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Key Concepts

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

Excited States
In atomic physics, an excited state of an atom occurs when one or more of its electrons are in an energy level higher than the lowest possible energy levels, known as ground states. Electrons in atoms can be excited to these higher energy levels in a variety of ways, including absorption of photons or collisions with other particles. An excited state has more energy and is generally less stable than the ground state.

For example, in the electron configuration \(1s^2 2s^2 3p^2 4p^1\), an electron from a lower energy level has been moved up to a higher level (4p). This creates an excited state since it's not the lowest possible energy arrangement for the electrons. Identifying these excited states can help us understand the processes that atoms undergo when they absorb energy.
Ground-State Condensed Configuration
The ground-state electron configuration of an atom is its most stable arrangement, where all electrons are in the lowest possible energy levels. When electrons are in the ground state, there are no electrons in "excited" orbitals, meaning each is as close to the nucleus as the quantum mechanical rules allow.

For example, the ground-state configuration for nitrogen (N) with 7 electrons is \(1s^2 2s^2 2p^3\). This arrangement represents the electrons occupying the lowest energy orbitals available. In contrast to excited states, the ground-state does not have electrons elevated to higher energy levels when lower energy levels are not completely filled. This makes the atom in the ground state more stable compared to when it鈥檚 in an excited state.
Periodic Table Elements
The periodic table is a systematic arrangement of elements based on atomic numbers and their electron configurations. Each element on the periodic table is defined by its atomic number, which equals the number of protons and, in a neutral atom, also the number of electrons.

In the context of the exercise:
  • Nitrogen (N) has 7 electrons and is situated in Group 15 of the periodic table.
  • Selenium (Se) with 34 electrons, is located in Group 16, a group known for its chemical reactivity due to having six valence electrons.
  • Rhodium (Rh), with 45 electrons, is found in Group 9, known for its use in catalytic converters and jewelry.
The periodic table helps predict the ground-state configuration of elements and provides insights into their chemical properties and behavior.
Electron Counting
Electron counting involves determining the number of electrons present in an atom or ion. This is essential in identifying elements from their electron configurations and understanding how elements will interact with each other chemically.

In the provided exercise, electron counting was used to determine the true identity of the element given its excited electron configuration. For example:
  • With a configuration \(1s^2 2s^2 3p^2 4p^1\), counting gives a total of 7 electrons, matching nitrogen.
  • The configuration \([Ar] 3d^{10} 4s^1 4p^4 5s^1\) totals 34 electrons, corresponding to selenium.
  • For \([Kr] 4d^6 5s^2 5p^1\), counting leads to 45 electrons, which is rhodium.
Properly counting electrons helps ensure the correct identification of elements in various states and configurations.

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Most popular questions from this chapter

(a) Why does the Bohr model of the hydrogen atom violate the uncertainty principle? (b) In what way is the description of the electron using a wave function consistent with de Broglie's hypothesis? (c) What is meant by the term probability density? Given the wave function, how do we find the probability density at a certain point in space?

Sketch the shape and orientation of the following types of orbitals: (a) \(s,(b) p_{z},(c) d_{x y}\).

The energy from radiation can be used to cause the rupture of chemical bonds. A minimum energy of \(941 \mathrm{~kJ} / \mathrm{mol}\) is required to break the nitrogen-nitrogen bond in \(\mathrm{N}_{2}\). What is the longest wavelength of radiation that possesses the necessary energy to break the bond? What type of electromagnetic radiation is this?

When the spectrum of light from the Sun is examined in high resolution in an experiment similar to that illustrated in Figure 6.11, dark lines are evident. These are called Fraunhofer lines, after the scientist who studied them extensively in the early nineteenth century. Altogether, about 25,000 lines have been identified in the solar spectrum between \(2950 \AA\) and \(10,000 \AA\). The Fraunhofer lines are attributed to absorption of certain wavelengths of the Sun's "white" light by gaseous elements in the Sun's atmosphere. (a) Describe the process that causes absorption of specific wavelengths of light from the solar spectrum. (b) If a scientist wanted to know which Fraunhofer lines belonged to a given element, say neon, what experiments could she conduct here on Earth to provide data?

Give the numerical values of \(n\) and \(l\) corresponding to each of the following orbital designations: (a) \(3 p,(\) b) \(2 s\), (c) \(4 f\), (d) \(5 d\).
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