Question

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

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

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.

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.

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.

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.

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.

Key concepts

Quantum Number n

The principal quantum number, denoted as \( n \), is fundamental in understanding electron shells in atoms. This number determines the energy level and distance of the electron shell from the nucleus. It is always a positive integer, such as 1, 2, or 3.

• An electron in a shell with a lower quantum number (e.g., \( n = 1 \)) is closer to the nucleus.
• As \( n \) increases, the electron shell is farther away, raising the potential energy level of the electron.

In simpler terms, think of \( n \) as the shell number. The larger the value of \( n \), the more energetic and further out the electron is from the atom's center. This concept is crucial for explaining why electrons at different energy levels have varying stabilities.

Coulomb's Law

Coulomb's law plays a crucial role in explaining the forces between charged particles, namely the nucleus and electrons in this context. The law states that the attractive force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.\[ F = \frac{k \cdot q_1 \cdot q_2}{r^2} \]- \( F \) is the force between the charges.- \( k \) is Coulomb's constant.- \( q_1 \) and \( q_2 \) are the magnitudes of the charges.- \( r \) is the distance between the charges.Due to this law:

• Electrons closer to the nucleus (lower \( n \)) experience a stronger attractive force due to smaller distances (\( r \)).
• This strong attraction keeps these electrons more stable.
• Conversely, electrons in higher shells (higher \( n \)) are less bound due to increased \( r \), reducing the attraction.

This explains why electrons in lower energy levels (low \( n \)) are more securely held by the nucleus.

Shielding Effect

The shielding effect is an essential concept to understand why electrons in higher energy levels (higher \( n \)) are less stable. The effect occurs because inner-shell electrons block or "shield" the outer-shell electrons from the full attractive force of the nucleus.This phenomenon results in:

• Reduction in the effective nuclear charge felt by electrons in higher energy levels, making them less tightly bound.
• Electrons in outer shells experience a weaker attraction, contributing to their higher energy state and reduced stability.
• Consequently, these electrons are more easily excited and can move to even higher energy levels.

In essence, the shielding effect provides insight into how electron arrangement and interactions impact stability. It highlights why electrons closer to the nucleus are less affected by the presence of other electrons and maintain a more stable configuration.