Problem 18 - Chemistry and Chemical Reactivity

Question

Which of the following statements correctly describes the value of the effective nuclear charge, \(Z^{*},\) felt by (a) the \(2 s\) electron at a large distance from a Li atom? (i) \(\quad Z^{*}\) equals 1 (ii) \(Z^{*}\) is between 1 and 3 (iii) \(Z^{*}\) equals 3 (b) the \(2 s\) electron at its most probable distance from the nucleus of a Li atom? (i) \(\quad Z^{*}\) equals 1 (ii) \(Z^{*}\) is between 1 and 3 (iii) \(Z^{*}\) equals 3

Step-by-Step Solution

Answer

(a) (i) 1; (b) (ii) between 1 and 3.

Step 1: Understanding Effective Nuclear Charge

The effective nuclear charge, denoted as \(Z^{*}\), is the net positive charge experienced by an electron in an atom. Electrons feel this charge as the actual nuclear charge (total protons) minus the shielding effect of other electrons. In a Li atom, with an atomic number of 3, the nuclear charge is 3, but the electrons' shielding reduces this value for outer electrons.

Step 2: Calculating Effective Nuclear Charge for (a)

Consider the \(2s\) electron at a large distance from a Li atom. At large distances, electrons are effectively beyond the influence of inner electrons. In such cases, the \(2s\) electron encounters the nucleus with minimal shielding effect. As the outermost electron in a complete atom basically acts as if it is under the influence of just one proton, \(Z^{*}\) reduces close to 1.

Step 3: Answer for (a)

The correct answer for the \(2s\) electron at a large distance is the effective nuclear charge \(Z^{*}\) equals 1. Therefore, the correct choice is (i).

Step 4: Calculating Effective Nuclear Charge for (b)

Evaluate the \(2s\) electron at its most probable distance from the nucleus. In this situation, the \(2s\) electron feels the attraction of the nucleus minus the effect of the 1s electrons, which are closer and shield some of the nuclear charge. Thus, \(Z^{*}\) is between 1 and 3, as the \(2s\) electron is not fully shielded by the inner core \(1s\) electrons.

Step 5: Answer for (b)

The correct answer for the \(2s\) electron at its most probable distance from the nucleus is \(Z^{*}\) is between 1 and 3. Therefore, the correct choice is (ii).

Key Concepts

Shielding Effect

The shielding effect is a fundamental concept in understanding atomic structure. It involves inner electrons partially shielding outer electrons from the full attractive force of the protons in the nucleus. This occurs because inner-shell electrons repel outer-shell electrons, thereby reducing the full impact of the nuclear charge they would otherwise feel.

• Inner electrons act as a barrier, decreasing the effective nuclear charge felt by outer electrons.
• The degree of shielding depends on the distance and the number of inner-shell electrons.

This concept is crucial for calculating the effective nuclear charge. Especially in atoms with more than one electron shell, where the interplay between these electron layers greatly affects electron arrangement and behavior. In simple terms, the more inner electrons present, the greater the shielding effect, and hence the lower the effective nuclear charge felt by the outer electrons.

Atomic Structure

Atomic structure is all about how atoms are organized, including the nucleus, made of protons and neutrons, and the electrons surrounding it. Electrons orbit in specific shells or energy levels, determined by quantum mechanics.

• The nucleus is small, dense, and positively charged due to protons.
• Electrons move in areas called orbitals, which exist within different energy levels.

In atomic structure, the effective nuclear charge plays a significant role by dictating how strongly electrons are held within these energy levels. This charge can influence many properties of an element, such as its ionization energy and atomic radius. Therefore, understanding atomic structure helps us predict how elements will behave chemically.

2s Electron

The 2s electron in an atom like lithium is part of the second energy level and has a spherical orbital shape. Electrons in the 2s orbital are crucial because they follow the first set of electrons in the 1s orbital, which is closest to the nucleus.

• 2s electrons experience some shielding effect from 1s electrons.
• They are less tightly bound than electrons in the 1s orbital due to this shielding.

In lithium, the 2s electron is the only electron in the second shell, making it a focus when discussing electron shielding and effective nuclear charge. It provides insight into how electron arrangement influences an atom's properties, particularly in regards to how much nuclear charge it effectively feels.

Lithium Atom

A lithium atom is one of the simplest elements following hydrogen and helium in the periodic table. It has an atomic number of 3, which means three protons in its nucleus, and usually three electrons outside. These electrons are organized in two shells: two in the 1s orbital and one in the 2s orbital. - The 1s electrons are closest to the nucleus and provide the primary shielding for the 2s electron. - Lithium’s simplicity makes it an excellent example for studying basic atomic principles like the effective nuclear charge. The nuclear charge of lithium is 3 due to its three protons; however, because of the shielding effect caused by the 1s electrons, the 2s electron does not feel the full charge of 3 when it is close to the nucleus. Instead, it experiences a reduced effective nuclear charge, important for predicting lithium's chemical behavior.