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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Ch 41: Atomic Physics
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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Table of contents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
Chapter 41, Problem 11b
Identify the element for each of these electron configurations. Then determine whether this configuration is the ground state or an excited state. 1s2 2s2 2p6 3s2 3p6 4s2 3d2
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Step 1: Analyze the given electron configuration: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d². This configuration represents the distribution of electrons in the atomic orbitals of an element. The total number of electrons can be determined by summing the superscripts: 2 + 2 + 6 + 2 + 6 + 2 + 2 = 22 electrons.
Step 2: Use the periodic table to identify the element with 22 electrons. The atomic number of an element corresponds to the number of protons (and electrons in a neutral atom). An atomic number of 22 corresponds to the element Titanium (Ti).
Step 3: Determine whether the configuration is in the ground state or an excited state. In the ground state, electrons occupy the lowest available energy levels. For Titanium, the expected ground-state configuration is 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d², which matches the given configuration.
Step 4: Conclude that the given configuration is the ground state for Titanium (Ti), as all electrons are in their lowest possible energy levels according to the Aufbau principle, Hund's rule, and the Pauli exclusion principle.
Step 5: Summarize the findings: The element is Titanium (Ti), and the given electron configuration represents its ground state.
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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 is represented by a series of numbers and letters indicating the energy levels and types of orbitals occupied by electrons. Understanding electron configurations is essential for identifying elements and their chemical properties, as they dictate how atoms interact with one another.
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Ground State vs. Excited State
The ground state of an atom is its lowest energy configuration, where electrons occupy the lowest available energy levels. An excited state occurs when one or more electrons have absorbed energy and moved to higher energy levels. Distinguishing between these states is crucial for understanding atomic behavior, as excited states can lead to phenomena such as emission spectra.
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Periodic Table and Element Identification
The periodic table organizes elements based on their atomic number and electron configurations, allowing for easy identification of elements. Each element has a unique electron configuration that corresponds to its position in the table. By analyzing the given electron configuration, one can determine the element and its properties, including its reactivity and placement in the periodic table.
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Related Practice
Textbook Question
1.0×106 atoms are excited to an upper energy level at t = 0 s. At the end of 20 ns, 90% of these atoms have undergone a quantum jump to the ground state. What is the lifetime of the excited state?
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Textbook Question
Draw a series of pictures, similar to Figure 41.21, for the ground states of Ca, Ni, As, and Kr.
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Textbook Question
How many lines of atoms would you expect to see on the collector plate of a Stern-Gerlach apparatus if the experiment is done with (a) lithium and (b) beryllium? Explain.
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Textbook Question
An excited state of an atom has a 25 ns lifetime. What is the probability that an excited atom will emit a photon during a 0.50 ns interval?
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Textbook Question
Identify the element for each of these electron configurations. Then determine whether this configuration is the ground state or an excited state. 1s² 2s² 2p⁵
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