Domanda del libro di testo
An electron confined in a one-dimensional box is observed, at different times, to have energies of 12 eV, 27 eV, and 48 eV. What is the length of the box?
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Ch 38: Quantization
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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TOC.tableOfContents
- 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: 9780137344796Non è quello che usi tu?Cambia libro di testo
Capitolo 38, Problema 54a
The first three energy levels of the fictitious element X are shown in FIGURE P38.54. What is the ionization energy of element X?
Guida verificata passo dopo passo1
Step 1: Understand the concept of ionization energy. Ionization energy is the amount of energy required to completely remove an electron from the atom, moving it from its ground state to a state where it is free from the atom (essentially at an energy level of zero).
Step 2: Identify the ground state energy level of element X from the given figure. The ground state is the lowest energy level, typically denoted as E₁.
Step 3: Recognize that the ionization energy is the difference between the ground state energy (E₁) and the energy level of a free electron (which is 0 eV). This can be expressed mathematically as:
Step 4: Substitute the value of E₁ from the figure into the formula. Ensure the energy value is in the correct units (e.g., electron volts, eV).
Step 5: Interpret the result. The ionization energy is the positive value of the magnitude of E₁, as it represents the energy required to remove the electron from the atom.
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Ionization Energy
Ionization energy is the amount of energy required to remove an electron from an atom or ion in its gaseous state. It is a critical concept in understanding how atoms interact and form ions. The first ionization energy refers specifically to the energy needed to remove the outermost electron, and it can be determined from the energy levels of an atom.
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Percorso guidato
04:10
Intro to Energy & Types of Energy
Energy Levels
Energy levels, or electron shells, are regions around an atom's nucleus where electrons are likely to be found. Each energy level corresponds to a specific energy state, and electrons can move between these levels by absorbing or releasing energy. The difference in energy between these levels is crucial for calculating ionization energy.
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04:10Intro to Energy & Types of Energy
Energy Level Diagram
An energy level diagram visually represents the energy levels of electrons in an atom. It typically shows the energy levels as horizontal lines, with the lowest energy level at the bottom. By analyzing the diagram, one can determine the energy difference between levels, which directly relates to the ionization energy needed to remove an electron from the atom.
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08:07Work and PV Diagrams
Pratica correlata
Domanda del libro di testo
The absorption spectrum of an atom consists of the wavelengths 200 nm, 300 nm, and 500 nm. b. What wavelengths are seen in the atom’s emission spectrum?
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Domanda del libro di testo
A muon—a subatomic particle with charge −e and a mass 207 times that of an electron—is confined in a 15-pm-long, one-dimensional box. ( 1pm=1picometer=10−12 m.) What is the wavelength, in nm, of the photon emitted in a quantum jump from n = 2 to n = 1?
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Domanda del libro di testo
The first three energy levels of the fictitious element X are shown in FIGURE P38.54. What wavelengths are observed in the absorption spectrum of element X? Express your answers in nm.
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Domanda del libro di testo
The first three energy levels of the fictitious element X were shown in Figure P38.54. An electron with a speed of 1.4×106 m/s collides with an atom of element X. Shortly afterward, the atom emits a photon with a wavelength of 1240 nm. What was the electron’s speed after the collision? Assume that, because the atom is much more massive than the electron, the recoil of the atom is negligible. Hint: The energy of the photon is not the energy transferred to the atom in the collision.
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Domanda del libro di testo
An electron confined in a one-dimensional box emits a 200 nm photon in a quantum jump from n = 2 to n = 1. What is the length of the box?
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