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Chapter 3: Problem 102

Identify the element whose condensed electron configuration is \([\mathrm{Ne}] 3 s^{2} 3 p^{3} .\) How many unpaired electrons are there in the ground state of this atom?

Short Answer

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Question: Identify the element with the condensed electron configuration [Ne]3s^2 3p^3 and determine the number of unpaired electrons in its ground state. Answer: The element is Phosphorus (P), and it has 3 unpaired electrons in its ground state.

Step by step solution

01

Write the full electron configuration from the condensed form

The given electron configuration is \([\mathrm{Ne}]3 s^{2} 3 p^{3}.\) The electron configuration of a neutral Neon atom is \(1 s^{2} 2 s^{2} 2 p^{6}\). Replace \([\mathrm{Ne}]\) with the full electron configuration of Neon to obtain the full electron configuration of the unknown element: \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{3}\).
02

Identify the element

Compare the electron configuration with the periodic table to identify the element. Count the total number of electrons: \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{3}\) has 2+2+6+2+3=15 electrons. An atom with 15 electrons has an atomic number of 15, which corresponds to Phosphorus (P).
03

Determine the number of unpaired electrons

Lastly, analyze the given electron configuration: \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{3}\). All electron orbitals with 2 electrons are considered to be paired. Therefore, the unpaired electrons are in the \(3 p^{3}\) subshell. The \(p\) subshell can hold a maximum of 6 electrons with the electron configuration \(p^{6}\). Since there are only 3 electrons present in this subshell, there are 3 unpaired electrons. In conclusion, the element with the condensed electron configuration \([\mathrm{Ne}] 3 s^{2} 3 p^{3}\) is Phosphorus (P), and it has 3 unpaired electrons in its ground state.

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Key Concepts

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

Unpaired Electrons
In an atom, electrons occupy different orbitals. Each orbital can hold a maximum of two electrons with opposite spins. When an orbital has only one electron, this electron is unpaired, which often results in magnetic properties. To determine unpaired electrons, focus on the outermost subshells where electrons are added according to Hund's Rule.
  • If the subshell is not filled, there may be unpaired electrons.
  • For example, a p-subshell can hold up to six electrons, filling the orbitals as three pairs.
  • In the case of Phosphorus, with the configuration \(3p^3\), there are three electrons in the p-subshell, each occupying a separate orbital without any pairing yet.
In conclusion, Phosphorus, with an electron configuration of \([\text{Ne}] 3s^2 3p^3\), has three unpaired electrons.
Ground State
The ground state of an atom refers to its most stable, lowest energy configuration. This is the natural resting state of electrons in an atom when it is not excited by external energy sources. Each atom naturally settles into its ground state by filling its electron orbitals in order of increasing energy levels.
  • The electron configuration is sequential, beginning with the lowest energy s-orbital.
  • Electrons fill the available orbitals following the Aufbau Principle, Hund's Rule, and the Pauli Exclusion Principle.
  • In Phosphorus, the ground state ends at \(3s^2 3p^3\), with the p-orbital forming its outermost electron shell.
Understanding the ground state configuration is essential for predicting the chemical properties and reactivity of the element.
Atomic Number
The atomic number of an element is fundamental to its identity. It is defined as the number of protons in the nucleus of an atom, which also equals the number of electrons in a neutral atom. This number is crucial because it determines the element's position on the periodic table and its chemical properties.
  • For Phosphorus, the atomic number is 15, indicating there are 15 protons and, in a neutral state, 15 electrons.
  • The electron configuration directly relates to the atomic number by filling orbitals with electrons up to the atomic number total.
  • Thus, for Phosphorus, the electron configuration, \(1s^2 2s^2 2p^6 3s^2 3p^3\), sums to 15 electrons, matching its atomic number.
The atomic number is not just a numerical value; it provides insight into the element's electron arrangement and reactivity.

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Most popular questions from this chapter

How many electrons could occupy orbitals with the following quantum numbers? a. \(n=2, \ell=0\) b. \(n=3, \ell=1, m_{\ell}=0\) c. \(n=4, \ell=2\) d. \(n=1, \ell=0, m_{\ell}=0\)

Using only the periodic table, arrange each set of particles by size, largest to smallest: a. \(\mathrm{Li}, \mathrm{B}, \mathrm{N}, \mathrm{Ne}\) b. \(\mathrm{Mg}, \mathrm{K}, \mathrm{Ca}, \mathrm{Sr}\) \(\mathrm{c} . \mathrm{Rb}^{+}, \mathrm{Sr}^{2+}, \mathrm{Cs}, \mathrm{Fr}\) \(\mathrm{d} . \mathrm{S}^{2-}, \mathrm{Cl}^{-}, \mathrm{Ar}, \mathrm{K}^{+}\)

Explain the difference between a ground-state \(\mathrm{H}\) atom and an excited-state H atom.

Two objects are moving at the same speed. Which (if any) of the following statements about them are true? a. The de Broglie wavelength of the heavier object is longer than that of the lighter one. b. If one object has twice as much mass as the other, then its wavelength is one-half the wavelength of the other. c. Doubling the speed of one of the objects will have the same effect on its wavelength as doubling its mass.

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