Problem 38 - Chemistry and Chemical Reactivity

Question

Identify the element that corresponds to each of the simplified photoelectron spectral data given below. (Energy data taken from D. A. Shirley, R. L. Martin, S. P. Kowalczyk, F. R. McFeely, and L. Ley: "Core-electron binding energies of the first thirty elements," Physical Review B, Vol. 15, pp. 544-552, \(1977 .)\) (a) There are peaks at energies corresponding to \(1079,70.8,38.0,5.14 \mathrm{eV},\) corresponding to 2 \(2,6,\) and 1 electrons, respectively. (b) There are peaks at energies corresponding to \(4043,443,351,48.4,30.1,\) and \(6.11 \mathrm{eV},\) corre- sponding to \(2,2,6,2,6,\) and 2 electrons, respectively. (c) There are peaks at energies corresponding to \(5475,638,524,77,47,12,\) and \(7.3 \mathrm{eV},\) corre- sponding to \(2,2,6,2,6,3,\) and 2 electrons, respectively.

Step-by-Step Solution

Answer

(a) Sodium, (b) Calcium, (c) Scandium.

Step 1: Understanding the Problem

The problem presents photoelectron spectral data with peaks that can be linked to the electron configurations of elements. Our task is to match this data to the correct elements based on known electron binding energies.

Step 2: Analyzing Data Set (a)

For the first element, we have peaks at energies of 1079, 70.8, 38.0, and 5.14 eV, corresponding to 2, 6, and 1 electrons. This configuration matches the 1s, 2s, 2p, and 3s subshells of Sodium (Na), which has the electron configuration 1s² 2s² 2p⁶ 3s¹.

Step 3: Analyzing Data Set (b)

The second set has peaks at energies 4043, 443, 351, 48.4, 30.1, and 6.11 eV, corresponding to 2, 2, 6, 2, 6, and 2 electrons. This corresponds to the 1s, 2s, 2p, 3s, 3p, and 4s subshells, fitting the electron configuration of Calcium (Ca), 1s² 2s² 2p⁶ 3s² 3p⁶ 4s².

Step 4: Analyzing Data Set (c)

The third set has peaks at energies of 5475, 638, 524, 77, 47, 12, and 7.3 eV, corresponding to 2, 2, 6, 2, 6, 3, and 2 electrons. This matches the 1s, 2s, 2p, 3s, 3p, 3d, and 4s subshells of Scandium (Sc), with an electron configuration of 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹ 4s².

Key Concepts

Electron Configuration

Electron configuration is a representation of the arrangement of electrons distributed among the orbitals of an atom. Normally, electrons fill the lowest energy levels first, which is known as the Aufbau principle. Electron configurations can be expressed through notations like 1s², 2s² 2p⁶, etc., where numbers represent energy levels, letters stand for sublevels or orbitals, and superscripts denote the number of electrons in those orbitals.

• Orbitals: s, p, d, and f orbitals are the fundamental types, with s holding 2, p holding 6, d holding 10, and f holding 14 electrons.
• Order of Filling: Electrons fill orbitals in the order of increasing energy: 1s, 2s, 2p, 3s, 3p, and so on.
• Stability: A fully filled or half-filled orbital offers additional stability to an electron configuration.

Understanding electron configurations allows us to explain many properties of elements, such as their chemical reactivity and the types of compounds they can form.

Binding Energy

Binding energy in the context of photoelectron spectroscopy refers to the energy needed to eject an electron from its orbital in an atom. This energy is usually measured in electron volts (eV) and can provide insights into the core levels of electrons in various elements. The greater the binding energy, the more tightly the electron is held by the nucleus.

• Significance: Binding energy is crucial in identifying elements because each element has a unique set of core-electron binding energies.
• Trends: Generally, moving across a period in the periodic table, binding energies increase due to increased nuclear charge.
• Shielding Effect: Inner electrons shield outer electrons from the full effect of the nucleus, impacting binding energies.

Knowledge of binding energies helps scientists use photoelectron spectroscopy to determine the elemental composition of materials.

Chemical Elements

Chemical elements are pure substances consisting of only one type of atom and are the simplest forms of matter with unique chemical properties. Elements are organized according to atomic number in the periodic table, reflecting the number of protons in the nucleus.

• Atomic Number: Identifies the number of protons in an atom. For example, Sodium (Na) has an atomic number of 11.
• Groups and Periods: Elements are arranged in groups (vertical columns) and periods (horizontal rows) which show recurring properties.
• Determinants of Reactivity: Electron configuration mainly determines chemical reactivity and bonding.

Understanding elements and their properties is foundational in the field of chemistry, allowing for the prediction of how different substances interact.

Core-electron Spectral Data

Core-electron spectral data refers to the information obtained from the analysis of an element's core electrons using photoelectron spectroscopy. The technique is used to explore the electronic structure of atoms by measuring the energies of electrons ejected by X-ray or UV light.

• Core versus Valence Electrons: Core electrons are those not involved in bonding, whereas valence electrons participate in chemical interactions.
• Photoelectron Peaks: The peaks observed correspond to specific electrons being ejected from their orbitals, and their energies help identify the element.
• Application: This analysis is crucial in applications such as material science, where understanding the electronic environment of atoms is essential.

Core-electron spectral data analysis allows for the determination of elemental and electronic structure, aiding both practical and theoretical studies in chemistry and physics.