Textbook Question
A hydrogen atom has orbital angular momentum 3.65 × 10⁻³⁴ J s. What is the atom's minimum possible energy? Explain.
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35. Special Relativity
Inertial Reference Frames
Problem 13
Textbook Question
Draw a series of pictures, similar to Figure 41.21, for the ground states of Ca, Ni, As, and Kr.
Verified step by step guidance1
Understand the problem: The question asks us to represent the ground-state electron configurations of the elements Calcium (Ca), Nickel (Ni), Arsenic (As), and Krypton (Kr) using diagrams similar to Figure 41.21. These diagrams typically involve filling electron orbitals (s, p, d, f) according to the Aufbau principle, Hund's rule, and the Pauli exclusion principle.
Step 1: Recall the Aufbau principle. Electrons fill orbitals starting from the lowest energy level to the highest. The order of filling is: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, etc. Use this sequence to determine the electron configuration for each element.
Step 2: Apply Hund's rule and the Pauli exclusion principle. Hund's rule states that electrons will fill degenerate orbitals (orbitals of the same energy level) singly before pairing up. The Pauli exclusion principle states that no two electrons in the same orbital can have the same spin.
Step 3: Write the electron configurations for each element: (a) Calcium (Ca, Z=20): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s². (b) Nickel (Ni, Z=28): 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁸ 4s². (c) Arsenic (As, Z=33): 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s² 4p³. (d) Krypton (Kr, Z=36): 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s² 4p⁶.
Step 4: Draw the orbital diagrams for each element. Represent each orbital as a box and each electron as an arrow (↑ or ↓). For example, for Calcium, the 4s orbital will have two arrows (↑↓), while the 3d orbitals will remain empty. Follow this approach for all elements, ensuring the correct number of electrons are placed in each orbital according to the rules.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Electron Configuration
Electron configuration describes the distribution of electrons in an atom's orbitals. It follows the Aufbau principle, which states that electrons fill the lowest energy orbitals first, and is crucial for understanding the chemical properties and reactivity of elements. For example, the ground state electron configuration of calcium (Ca) is 1s² 2s² 2p⁶ 3s², indicating its two outermost electrons in the 3s orbital.
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Ground State
The ground state of an atom refers to the lowest energy configuration of its electrons, where they occupy the closest orbitals to the nucleus. This state is significant because it determines the atom's stability and its behavior in chemical reactions. For instance, the ground state of nickel (Ni) is 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁸ 4s², reflecting its filled and partially filled orbitals.
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Periodic Trends
Periodic trends refer to the predictable patterns observed in the properties of elements as you move across or down the periodic table. These trends include atomic radius, ionization energy, and electronegativity, which are influenced by the arrangement of electrons. Understanding these trends helps in predicting the behavior of elements like arsenic (As) and krypton (Kr) based on their positions in the periodic table.
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