Problem 137 - Chemistry The Science in Context

Question

Effective nuclear charge \(\left(Z_{\text {eff }}\right)\) is related to atomic number (Z) by a parameter called the shielding parameter \((\sigma)\) according to the equation \(Z_{\mathrm{eff}}=Z-\sigma\) a. Calculate \(Z_{\mathrm{eff}}\) for the outermost s electrons of Ne and \(\mathrm{Ar}\) given \(\sigma=4.24\) (for \(\mathrm{Ne}\) ) and 11.24 (for \(\mathrm{Ar}\) ). b. Explain why the shielding parameter is much greater for Ar than for Ne.

Step-by-Step Solution

Answer

Question: Calculate the effective nuclear charge for the outermost s electrons of Ne and Ar, and explain why the shielding parameter is much greater for Ar than for Ne. Answer: The effective nuclear charge for Ne is 5.76, and for Ar, it is 6.76. The shielding parameter is greater for Ar than for Ne because of the presence of additional electron shells in Ar, which provide increased shielding of the outermost s electrons from the nucleus.

Step 1: Find the atomic numbers for Ne and Ar

To find the atomic numbers (Z) for Ne (Neon) and Ar (Argon), we can look them up in the periodic table. Neon is element number 10, so its atomic number is 10. Argon is element number 18, so its atomic number is 18.

Step 2: Calculate the effective nuclear charge for Ne and Ar

Using the given formula \(Z_{\text{eff}} = Z - \sigma\), we can calculate the effective nuclear charge for the outermost s electrons of Ne and Ar. For Ne: \(Z_{\text{eff}}(Ne) = Z(Ne) - \sigma_{Ne} = 10 - 4.24 = 5.76\) For Ar: \(Z_{\text{eff}}(Ar) = Z(Ar) - \sigma_{Ar} = 18 - 11.24 = 6.76\)

Step 3: Explain the difference in shielding parameters

The electron configurations of Ne and Ar differ due to the presence of additional electron shells in Ar. Ne has the electron configuration of \(1s^2 2s^2 2p^6\), while Ar has the electron configuration of \(1s^2 2s^2 2p^6 3s^2 3p^6\). The electrons in the inner shells of Ar, specifically the 2p electrons, shield the outermost s electrons from the nucleus more effectively than in Ne. As a result, the s electrons in Ar experience a lower effective nuclear charge due to the increased shielding by the inner electrons. This explains why the shielding parameter is larger for Ar than for Ne.

Key Concepts

Atomic Number

An atom's atomic number, denoted by the symbol \(Z\), is a fundamental property that defines the number of protons in the nucleus of an atom. This number is crucial because it determines the element's identity on the periodic table.

• Neon (Ne): The atomic number is 10. Thus, Neon has 10 protons.
• Argon (Ar): The atomic number is 18, meaning Argon has 18 protons.

The atomic number not only identifies the element but also gives insight into its electron configuration in a neutral atom, thereby directly affecting its chemical properties and behavior. As we look at atomic number in reactions and calculations, such as determining the effective nuclear charge, it plays a crucial role in defining how electrons are distributed around the nucleus. Remember: Higher atomic number usually means more electron shells, which can influence many properties of an element.

Shielding Parameter

The shielding parameter, represented by the symbol \(\sigma\), plays an essential role in understanding how inner electrons affect the attraction experienced by outer electrons from the nucleus. As electrons are negatively charged, they repel each other. Outer electrons are shielded from full nuclear charge by inner shell electrons, reducing the net positive charge experienced by the outermost electrons.

• More inner shells: More inner electron shells lead to greater shielding as they provide more thorough blocking of nuclear charge from the outer electrons.
• Neon vs. Argon: In the example of Ne versus Ar, Ar's shielding parameter is higher due to its more extensive electron arrangement with additional inner shells compared to Ne.

The shielding parameter is significant because it directly correlates with how tightly an atom holds its outer electrons. A higher \(\sigma\) means more shielding, and hence a lower effective nuclear charge \(Z_{\text{eff}}\). This influences the atom's ability to interact with other elements.

Electron Configuration

Electron configuration reflects the distribution of electrons of an atom or molecule in its atomic or molecular orbitals. Understanding the electron configuration helps explain the chemical and physical properties of elements. Let's consider Neon and Argon.

• Neon (Ne): \(1s^2 2s^2 2p^6\). Neon has a complete second energy level, making it stable and inert.
• Argon (Ar): \(1s^2 2s^2 2p^6 3s^2 3p^6\). Argon adds an additional energy level, which contributes to its higher shielding parameter.

The presence of more energy levels – as seen in Argon – leads to the enhanced shielding seen in these elements. This is because inner electrons occupy lower energy levels and block the nucleus' pull from outer electrons. Thus, while both Ne and Ar are noble gases known for their stability and lack of reactivity, their electron configurations help illustrate why Ar has a significantly larger shielding parameter than Ne.