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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) \(\mathrm{ls}^{2} 2 \mathrm{~s}^{2} 3 p^{2} 4 p^{1}\), (b) \([\mathrm{Ar}] 3 d^{10} 4 s^{1} 4 p^{4} 5 s^{1}\), (c) \([\mathrm{Kr}] 4 d^{6} 5 s^{2} 5 p^{1}\)

Short Answer

Expert verified
The ground-state condensed electron configurations for the given excited electron configurations are: a) Nitrogen (N): \(1s^{2} 2s^{2} 2p^{3}\) b) Selenium (Se): \([\mathrm{Ar}] 3d^{10} 4s^{2} 4p^{4}\) c) Rhodium (Rh): \([\mathrm{Kr}] 4d^{7} 5s^{1}\)

Step by step solution

01

Count electrons in the excited state

For each subshell, count the electrons and add them up. a) \(1s^{2} 2s^{2} 3p^{2} 4p^{1}\): 2 + 2 + 2 + 1 = 7 electrons b) \([\mathrm{Ar}] 3d^{10} 4s^{1} 4p^{4} 5s^{1}\): 18 (Ar) + 10 + 1 + 4 + 1 = 34 electrons c) \([\mathrm{Kr}] 4d^{6} 5s^{2} 5p^{1}\): 36 (Kr) + 6 + 2 + 1 = 45 electrons
02

Identify elements in the periodic table

Based on the total number of electrons, we can find the corresponding elements. a) Element with 7 electrons: Nitrogen (N) b) Element with 34 electrons: Selenium (Se) c) Element with 45 electrons: Rhodium (Rh)
03

Write ground-state condensed electron configurations

Write the ground-state electron configurations for the identified elements in condensed form. a) Nitrogen (N): \(1s^{2} 2s^{2} 2p^{3}\) b) Selenium (Se): \([\mathrm{Ar}] 3d^{10} 4s^{2} 4p^{4}\) c) Rhodium (Rh): \([\mathrm{Kr}] 4d^{7} 5s^{1}\) In conclusion, the ground-state condensed electron configurations for the given excited electron configurations are: a) Nitrogen (N): \(1s^{2} 2s^{2} 2p^{3}\) b) Selenium (Se): \([\mathrm{Ar}] 3d^{10} 4s^{2} 4p^{4}\) c) Rhodium (Rh): \([\mathrm{Kr}] 4d^{7} 5s^{1}\)

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Key Concepts

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

Excited State
Atoms exist in different energy levels, and the arrangement of electrons can change due to energy absorption. When an electron in an atom absorbs energy, it can move to a higher energy level. This energy-driven change in electron configuration results in what we call an 'excited state'. It is important to note that excited states are not stable and are temporary until the electron returns to its original, lower energy level. This return process often results in the release of energy, typically in the form of light.
  • In an excited state, electrons are in higher energy orbitals than in their most stable positions.
  • It's the absorption of additional energy that causes electrons to jump up to higher levels.
  • Excited states are useful in understanding phenomena such as atomic spectra and chemical reactions.
Ground-State Electron Configuration
The ground-state electron configuration is the arrangement of electrons in an atom at its lowest energy state. Essentially, this is how electrons naturally distribute among the various atomic orbitals when the atom is not energized. Determining the ground-state configuration provides a baseline for identifying any excited states. In a ground-state configuration, electrons fill orbitals starting from the lowest energy level and moving upward. The typical order follows the Aufbau principle, Hund's Rule, and Pauli Exclusion Principle, which help to explain the filling process.
  • Aufbau Principle: Electrons occupy the lowest energy orbitals available.
  • Hund's Rule: Electrons fill degenerate orbitals singly before pairing up.
  • Pauli Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers.
Periodic Table
The periodic table is a vital tool for understanding electron configurations. It not only organizes elements in order of increasing atomic number but also groups them by their chemical properties, which relate closely to their electron configurations. Each row, or period, in the table reflects a filling of a particular electron shell, while each column, or group, generally shares common valence electron configurations. Understanding the periodic table allows you to predict the electron configuration of any given element and identify trends in atomic radii, electronegativity, and ionization energy. For example:
  • Elements in the same group often have similar valence electron configurations.
  • Moving left to right across a period, the atomic number increases, adding electrons sequentially.
  • The periodic table is divided into blocks (s, p, d, and f) based on the subshell that is being filled.
Electrons
Electrons are negatively charged particles that revolve around the nucleus of an atom in various orbitals. These tiny particles play a crucial role in chemical bonding and reactions, since they can be shared, transferred, or rearranged between atoms. Their distribution in the atomic orbitals determines the chemical behavior and properties of an element. Here are a few key points:
  • Electrons reside in energy levels or shells around the nucleus, where each shell can hold a specific maximum number of electrons.
  • Electron configurations determine the atom's state鈥攊n particular, whether it is in an excited or ground state.
  • Changes in electron configuration, especially in the outermost electrons (valence electrons), are what drive chemical reactions.
Electrons are dynamic and key to understanding not just chemical identities, but also processes such as electricity, magnetism, and light interactions.

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Most popular questions from this chapter

A diode laser emits at a wavelength of \(987 \mathrm{~nm}\). (a) In what portion of the electromagnetic spectrum is this radiation found? (b) All of its output energy is absorbed in a detector that measures a total energy of \(0.52\) J over a period of \(32 \mathrm{~s}\). How many photons per second are being emitted by the laser?

In the television series Star Trek, the transporter beam is a device used to "beam down" people from the Starship Enterprise to another location, such as the surface of a planet. The writers of the show put a "Heisenberg compensator" into the transporter beam mechanism. Explain why such a compensator would be necessary to get around Heisenberg's uncertainty principle.

(a) The average distance from the nucleus of a 3 s electron in a chlorine atom is smaller than that for a \(3 p\) electron. In light of this fact, which orbital is higher in energy? (b) Would you expect it to require more or less energy to remove a \(3 s\) electron from the chlorine atom, as compared with a \(2 p\) electron? Explain.

Consider a fictitious one-dimensional system with one electron. The wave function for the electron, drawn at the top of the next column, is \(\psi(x)=\sin x\) from \(x=0\) to \(x=2 \pi .\) (a) Sketch the probability density, \(\psi^{2}(x)\), from \(x=0\) to \(x=2 \pi\) (b) At what value or values of \(x\) will there be the greatest probability of finding the electron? (c) What is the probability that the electron will be found at \(x=\pi ?\) What is such a point in a wave function called? \([\) Section \(6.5]\)

The electron microscope has been widely used to obtain highly magnified images of biological and other types of materials. When an electron is accelerated through a particular potential field, it attains a speed of \(9.38 \times 10^{6} \mathrm{~m} / \mathrm{s}\). What is the characteristic wavelength of this electron? Is the wavelength comparable to the size of atoms?
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