Textbook Question
Draw an energy-level diagram, similar to Figure 38.21, for the He+ ion. On your diagram: Show the ionization limit.
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Ch 38: Quantization
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 38, Problem 63a
Draw an energy-level diagram, similar to Figure 38.21, for the He+ ion. On your diagram: Show the first five energy levels. Label each with the values of n and En.
Verified step by step guidance1
Understand the context: The He+ ion is a hydrogen-like ion with a single electron orbiting a nucleus of charge +2e. The energy levels for such ions are determined using the formula for the energy of hydrogen-like atoms: , where Z is the atomic number (Z = 2 for He+) and n is the principal quantum number.
Calculate the energy levels: Use the formula to calculate the first five energy levels (n = 1, 2, 3, 4, 5). Substitute Z = 2 into the formula and compute the energy for each value of n.
Label the energy levels: For each energy level, write the corresponding value of n (e.g., n = 1, n = 2, etc.) and the calculated energy . Ensure the energy values are negative, as they represent bound states of the electron.
Draw the energy-level diagram: On a vertical axis, represent energy (with more negative values lower on the axis). Plot horizontal lines for each energy level, spacing them according to the calculated energy differences. Label each line with its corresponding n value and energy .
Add clarity to the diagram: Ensure the diagram is neat and clearly labeled. Indicate that the energy levels get closer together as n increases, reflecting the fact that the energy difference between successive levels decreases as n becomes larger.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Energy Levels in Hydrogen-like Atoms
In hydrogen-like atoms, such as He+, energy levels are quantized and determined by the principal quantum number (n). The energy of each level can be calculated using the formula En = -Z² * 13.6 eV / n², where Z is the atomic number. For He+, Z = 2, leading to distinct energy values for each level as n increases.
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Quantum Numbers
Quantum numbers are values that describe the unique quantum state of an electron in an atom. The principal quantum number (n) indicates the energy level and size of the orbital, while the azimuthal (l) and magnetic (m) quantum numbers describe the shape and orientation of the orbital. For energy-level diagrams, only n is typically labeled.
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Energy-Level Diagrams
Energy-level diagrams visually represent the allowed energy states of electrons in an atom. Each horizontal line corresponds to a specific energy level, labeled with its quantum number (n) and energy (En). These diagrams help illustrate transitions between energy levels, which are fundamental to understanding atomic spectra and electron behavior.
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Related Practice
Textbook Question
Very large, hot stars—much hotter than our sun—can be identified by the way in which He+ ions in their atmosphere absorb light. What are the three longest wavelengths, in nm, in the Balmer series of He+?
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Textbook Question
Consider a hydrogen atom in stationary state n. On average, an atom stays in the n = 2 state for 1.6 ns before undergoing a transition to the n = 1 state. On average, how many revolutions does the electron make before the transition?
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Textbook Question
Draw an energy-level diagram, similar to Figure 38.21, for the He+ ion. On your diagram: Show all possible emission transitions from the n = 4 energy level.
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Textbook Question
What is the difference in the wavelengths emitted in a 199→2 transition and a 200→2 transition?
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Textbook Question
What wavelength photon does a hydrogen atom emit in a 200→199 transition?
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