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Chapter 5: Problem 89

Predict which of these clements would have the greatest difference betwcen the first and sccond ionization cncrgics: Si, \(\mathrm{Na}, \mathrm{P}, \mathrm{Mg} .\) Bricfly explain your answer.

Short Answer

Expert verified
Sodium ( \(\text{Na}\)) has the greatest difference in ionization energies.

Step by step solution

01

Understanding Ionization Energies

Ionization energy is the energy required to remove an electron from an atom or ion in its gaseous state. The first ionization energy refers to removing the first electron, while the second ionization energy refers to removing the second electron.
02

Evaluating Ionization Energy Trends

In general, the second ionization energy is significantly higher than the first ionization energy for elements whose removal of a second electron requires disrupting a stable electronic configuration. This is because it would involve breaking into a filled or half-filled shell.
03

Examining the Electronic Configurations

Let's consider the electronic configurations of the elements: - Sodium (\( ext{Na}\)): 1s虏 2s虏 2p鈦� 3s鹿 - Silicon (\( ext{Si}\)): 1s虏 2s虏 2p鈦� 3s虏 3p虏 - Phosphorus (\( ext{P}\)): 1s虏 2s虏 2p鈦� 3s虏 3p鲁 - Magnesium (\( ext{Mg}\)): 1s虏 2s虏 2p鈦� 3s虏. The key is to determine which element will have a stable configuration after the removal of the first electron and thus a greater increase in ionization energy for the second electron.
04

Identifying the Greatest Energy Difference

Sodium (\( ext{Na}\)) has a configuration of 1s虏 2s虏 2p鈦� 3s鹿. Removing the first electron leaves it with a stable, filled, 2s虏 2p鈦� configuration. However, removing the second electron would mean breaking into this stable configuration, resulting in a large increase in ionization energy between the first and second ionization.
05

Conclusion

Based on electronic configuration analysis, sodium (\( ext{Na}\)) is expected to have the greatest difference between the first and second ionization energies among the given elements as it reaches a noble gas configuration with the removal of the first electron.

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Key Concepts

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

First Ionization Energy
The first ionization energy is the energy needed to remove the first electron from an atom. Imagine trying to pull a basketball out from a tight rack. The first ball might come out easily if the grip isn't too strong.
In the case of atoms, this energy depends on the attraction between the electrons and the nucleus. The stronger the attraction, the more energy is required.
  • This process turns a neutral atom into a positively charged ion.
  • For sodium ( Na ), the first ionization energy involves removing the 3s鹿 electron, leaving behind a stable, noble gas configuration, 1s虏 2s虏 2p鈦�.
Understanding first ionization energy is critical because it tells us how tightly electrons are held and how easily they can be removed.
Second Ionization Energy
The second ionization energy is the energy required to remove another electron from an already positively charged ion. Continuing with our basketball analogy, the second ball is often wedged tighter, making it harder to remove.
  • Typically, the second ionization energy is higher than the first because you're removing an electron from an already positive ion, which means it feels an even greater pull toward the nucleus.
  • For sodium, after the 3s鹿 electron is removed, what remains is a stable, complete 2s虏 2p鈦� shell. Breaking into this shell requires much more energy, hence a much higher second ionization energy.
The significant jump from first to second ionization energy is due to potentially disrupting this stable configuration.
Electronic Configuration
Electronic configuration refers to the arrangement of electrons in an atom's orbitals. Think of it as the blueprint outlining where each electron lives within the atom's house.
  • It's written in a notation combining energy levels, sublevels, and the number of electrons, like 1s虏 2s虏 2p鈦� for sodium's ion.
  • Understanding electronic configuration helps predict chemical behavior, including ionization energies.
  • A stable configuration, like sodium's 1s虏 2s虏 2p鈦� after first ionization, is why its second ionization energy jumps significantly.
Knowing the electronic configuration is essential to understanding why some atoms release electrons easily, while others hold onto them tightly.
Stable Configuration
A stable configuration occurs when electrons fill an energy level, making the atom energetically favored. Consider a perfectly balanced tower of blocks; moving just one might destabilize the entire structure.
  • In atomic terms, a filled or half-filled shell represents stability.
  • This stability explains why atoms like sodium show a massive increase in ionization energy upon removing a second electron because you're disturbing a completed 2p level.
Reaching a stable electronic configuration often resembles noble gases, which is why elements close to them energetically strive for such arrangements.

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Most popular questions from this chapter

To eject electrons from the surface of potassium metal requires a minimum energy of \(3.68 \times 10^{-19} \mathrm{~J}\). When \(600 .-\mathrm{nm}\) photons shine on a potassium surface, will they cause the photoelectric effect? Explain.

Calculate the energy and wavelength of the photon associated with the electron transition from \(n=2\) to \(n=5\) in the hydrogen atom.

A certain minimum energy, \(E_{\text {min }}\) is required to eject an electron from a photosensitive surface. Any energy absorbed beyond this minimum gives kinctic cnergy to the cjected clectron. When \(540 .-\mathrm{nm}\) light falls on a cesium surface, an electron is ejected with a kinctic energy of \(6.69 \times 10^{-20} \mathrm{~J}\). When the wavelength is \(400 \mathrm{nm}\), the kinctic cnergy is \(1.96 \times 10^{-19} \mathrm{~J}\). (a) Calculate \(E_{\text {min }}\) for cesium, in joules. (b) Calculate the longest wavelength, in nanometers, that will eject an electron from cesium.

Calculate the energy and the wavelength of the photon associated with an electron transition from \(n=1\) to \(n=4\) in the hydrogen atom.

From memory, sketch the shape of the boundary surface for each of these atomic orbitals: (a) \(2 p_{z}\) (b) \(4 s\) (c) \(3 d_{x y}\)
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