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Chapter 4: Problem 7

Why is an electron in a shell that has a low value of \(n\) in a more stable arrangement than one in a shell that has a higher value of \(n\) ?

Short Answer

Expert verified
Electrons in shells with low n values are more stable than those in shells with higher n values due to two factors: 1) They are closer to the nucleus and experience a stronger attractive force according to Coulomb's law, and 2) Electrons in lower energy shells shield those in higher energy shells from the nucleus's attractive force, making higher n electrons less stable. As a result, an electron in a shell with a low value of n is in a more stable arrangement than one in a shell with a higher value of n.

Step by step solution

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1. Understanding Electron Shells and Quantum Number n

Electrons are found in specific regions around an atom's nucleus called electron shells, also known as energy levels. Each shell is characterized by a principal quantum number (n), where n is an integer value (1, 2, 3, ...). The higher the value of n, the further away the electron shell is from the nucleus and the higher the energy level.
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2. Electron Stability and Energy Levels

An electron is considered stable if it has the lowest possible energy, which is a condition known as the ground state. When an electron absorbs energy, it moves to a higher energy shell, corresponding to a higher n value, and is considered in an excited state. However, electrons tend to eventually return to the ground state by losing the excess energy.
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3. Coulomb's Law and Nuclear Attraction

One reason for the stability of electrons in lower energy shells is explained by Coulomb's law. This law describes the attractive force between the positively charged nucleus and the negatively charged electrons. As the distance between the nucleus and the electron decreases, the attractive force between them increases. Thus, electrons in shells with lower n values are closer to the nucleus and experience a stronger attractive force, making them more stable.
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4. Shielding Effect

Another factor contributing to electron stability is the shielding effect. Electrons in lower energy levels (low n value) can shield or protect the electrons in higher energy levels from the nucleus's attractive force. This results in decreased attraction and stability for electrons in shells with higher n values.
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5. Conclusion

To sum up, electrons in shells with low n values are more stable than those in shells with higher n values because of the following factors: 1. They are closer to the nucleus and experience a stronger attractive force due to Coulomb's law. 2. Electrons in lower energy shells shield those in higher energy shells from the nucleus's attractive force, making higher n electrons less stable. Therefore, an electron in a shell with a low value of n is in a more stable arrangement than one in a shell with a higher value of n.

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