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(a) The doubly charged ion \(N^{2+}\) is formed by removing two electrons from a nitrogen atom. What is the ground-state electron configuration for the \(N^{2+}\) ion? (b) Estimate the energy of the least strongly bound level in the \(L\) shell of \(N^{2+}\). (c) The doubly charged ion \(P^{2+}\) is formed by removing two electrons from a phosphorus atom. What is the ground-state electron configuration for the \(P^{2+}\) ion? (d) Estimate the energy of the least strongly bound level in the \(M\) shell of \(P^{2+}\).

Short Answer

Expert verified
(a) \( 1s^2 2s^2 2p^1 \); (b) Roughly \(-54.4\) eV; (c) \( 1s^2 2s^2 2p^6 3s^2 3p^1 \); (d) Roughly \(-15.6\) eV.

Step by step solution

01

Understand the ground-state electron configuration of nitrogen and phosphorus

The ground-state electron configuration of a neutral nitrogen atom is \( 1s^2 2s^2 2p^3 \), and for phosphorus, it is \( 1s^2 2s^2 2p^6 3s^2 3p^3 \). We need these as starting points to find the configurations of their doubly charged ions.
02

Determine the electron configuration for \( N^{2+} \)

\( N^{2+} \) is formed by removing two electrons from a nitrogen atom. Starting from \( 1s^2 2s^2 2p^3 \), remove the two outermost 2p electrons. The resulting configuration is \( 1s^2 2s^2 2p^1 \).
03

Determine the electron configuration for \( P^{2+} \)

For \( P^{2+} \), remove the two outermost electrons from the phosphorus atom's configuration \( 1s^2 2s^2 2p^6 3s^2 3p^3 \). This results in \( 1s^2 2s^2 2p^6 3s^2 3p^1 \).
04

Estimate the energy of the least strongly bound level in the \( L \) shell of \( N^{2+} \)

The \( L \) shell involves electrons in the second energy level (\( 2s \) and \( 2p \)). With configuration \( 1s^2 2s^2 2p^1 \), the \( 2p \) electron is the least strongly bound. The energy can be estimated using the ionization approximation where energy levels depend on \( Z-1 \), where \( Z \) is the effective nuclear charge. For \( N^{2+} \), this may approximate to \(-13.6\left(\frac{6^2}{2^2}\right)\) eV, considering screening and reductions.
05

Estimate the energy of the least strongly bound level in the \( M \) shell of \( P^{2+} \)

The \( M \) shell involves electrons in the third energy level (\( 3s \) and \( 3p \)). For \( P^{2+} \) with configuration \( 1s^2 2s^2 2p^6 3s^2 3p^1 \), the \( 3p \) electron is least strongly bound. Estimate the energy using \( Z-2 \) for screening in phosphorous: \(-13.6\left(\frac{13-2}{3^2}\right)^2\) eV.

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Key Concepts

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

Ionization Energy
Ionization energy reveals how difficult it is to remove an electron from an atom or ion. When an element loses electrons, energy is required—a process known as ionization.
- The first ionization energy is the energy needed to remove the first electron. - Each subsequent electron removal requires more energy, known as the second ionization energy, third, and so on.
Why does each subsequent electron require more energy to remove? Because the ion becomes more positively charged, meaning it has a stronger attraction to the remaining electrons. This results in higher ionization energies for each electron removed.
It’s critical for understanding configurations like those of ions such as nitrogen and phosphorus, where removing multiple electrons significantly alters their state.
Nitrogen Ion
The nitrogen ion, specifically the doubly charged ion denoted as \( N^{2+} \), is formed by removing two electrons from a nitrogen atom. - A neutral nitrogen atom has an electron configuration of \( 1s^2 2s^2 2p^3 \).- When it becomes doubly ionized, the configuration changes to \( 1s^2 2s^2 2p^1 \) due to the removal of two \( 2p \) electrons.
This reduction reflects the significant change in energy and stability for the nitrogen ion, illustrating the effect of ionization energy and electron loss. The missing electrons can affect both the chemical reactivity and bonding characteristics of the nitrogen ion, compared to its neutral atom state.
Phosphorus Ion
The phosphorus ion \( P^{2+} \) is formed when two electrons are removed from a neutral phosphorus atom, which has a ground-state electron configuration of \( 1s^2 2s^2 2p^6 3s^2 3p^3 \). - Removing two electrons results in \( 1s^2 2s^2 2p^6 3s^2 3p^1 \).
This alteration in the electron configuration highlights the phosphorus ion's change in its properties. It demonstrates how electrons in the outer shell are typically removed first due to their higher energy levels and weaker attraction to the nucleus.# The consecutive removal requires understanding ionization energies.
A crucial consideration is that as phosphorus becomes more positively charged, its chemical reactivity and electron affinity are impacted proportionately.
Ground-State
The term "ground-state" refers to the most stable and lowest energy configuration of an atom's electrons. - In a neutral atom, electrons fill the lowest available energy levels first, following the Aufbau principle.- The ground-state configuration reflects the typical arrangement of electrons in an atom or ion at rest.
For ions like \( N^{2+} \) and \( P^{2+} \), ground-state configurations are revisited since electron removal shifts electrons into lower energy states, yet often remain in their respective shells (like L shell for nitrogen ion or M shell for phosphorus ion).
Understanding ground-state configurations is critical, as these are the starting points from which any excitation or ionization processes occur. They provide an essential reference for predicting an element or ion's chemical behavior and reactivity.

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Most popular questions from this chapter

A particle is in the three-dimensional cubical box of Section 41.2. (a) Consider the cubical volume defined by \(0 \leq x \leq L/4, 0 \leq y \leq L/4\), and \(0 \leq z \leq L/4\). What fraction of the total volume of the box is this cubical volume? (b) If the particle is in the ground state \((n_X = 1, n_Y = 1, n_Z = 1)\), calculate the probability that the particle will be found in the cubical volume defined in part (a). (c) Repeat the calculation of part (b) when the particle is in the state \(n_X = 2, n_Y = 1, n_Z = 1\).

For germanium (\(Ge, Z = 32\)), make a list of the number of electrons in each subshell (\(1s, 2s, 2p,\dots\)). Use the allowed values of the quantum numbers along with the exclusion principle; do not refer to Table 41.3.

A hydrogen atom in a 3\(p\) state is placed in a uniform external magnetic field \(\vec B\). Consider the interaction of the magnetic field with the atom's orbital magnetic dipole moment. (a) What field magnitude \(B\) is required to split the 3\(p\) state into multiple levels with an energy difference of 2.71 \(\times\) 10\(^{-5}\) eV between adjacent levels? (b) How many levels will there be?

You are studying the absorption of electromagnetic radiation by electrons in a crystal structure. The situation is well described by an electron in a cubical box of side length \(L\). The electron is initially in the ground state. (a) You observe that the longest-wavelength photon that is absorbed has a wavelength in air of \(\lambda\) = 624 nm. What is \(L\)? (b) You find that \(\lambda\) = 234 nm is also absorbed when the initial state is still the ground state. What is the value of \(n$$^2\) for the final state in the transition for which this wavelength is absorbed, where \(n$$^2\) = \(n$$_X^2\) + \(n$$_y^2\) + \(n$$_z^2\) ? What is the degeneracy of this energy level (including the degeneracy due to electron spin)?

In studying electron screening in multielectron atoms, you begin with the alkali metals. You look up experimental data and find the results given in the table. The ionization energy is the minimum energy required to remove the least-bound electron from a ground-state atom. (a) The units kJ/mol given in the table are the minimum energy in kJ required to ionize 1 mol of atoms. Convert the given values for ionization energy to the energy in eV required to ionize one atom. (b) What is the value of the nuclear charge \(Z\) for each element in the table? What is the n quantum number for the least-bound electron in the ground state? (c) Calculate \(Z$$_{eff}\) for this electron in each alkali-metal atom. (d) The ionization energies decrease as \(Z\) increases. Does \(Z$$_{eff}\) increase or decrease as \(Z\) increases? Why does \(Z$$_{eff}\) have this behavior?

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