Domanda del libro di testo
Prove that the normalization constant of the 2p radial wave function of the hydrogen atom is (24πaB3)-1/2, as shown in Equations 41.7. Hint: See the hint in Problem 32.
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Ch 41: Atomic Physics
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 41, Problema 27a
There exist subatomic particles whose spin is characterized by s = 1, rather than the s = ½ of electrons. These particles are said to have a spin of one. What is the magnitude ( as a multiple of ℏ ) of the spin angular momentum S for a particle with a spin of one?
Guida verificata passo dopo passo1
Understand the concept of spin angular momentum: The spin angular momentum of a particle is given by the formula \( S = \sqrt{s(s+1)} \hbar \), where \( s \) is the spin quantum number and \( \hbar \) is the reduced Planck's constant.
Identify the given spin quantum number: In this problem, the spin quantum number \( s \) is provided as \( s = 1 \).
Substitute the value of \( s \) into the formula: Replace \( s \) with 1 in the formula \( S = \sqrt{s(s+1)} \hbar \), resulting in \( S = \sqrt{1(1+1)} \hbar \).
Simplify the expression inside the square root: Calculate \( 1+1 \), which equals 2, so the formula becomes \( S = \sqrt{1 \cdot 2} \hbar \).
Simplify further to find the magnitude: The expression simplifies to \( S = \sqrt{2} \hbar \), which represents the magnitude of the spin angular momentum as a multiple of \( \hbar \).
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Concetti chiave
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Spin Angular Momentum
Spin angular momentum is a fundamental property of particles, akin to classical angular momentum, but it arises from quantum mechanical effects. It is quantized, meaning it can only take on certain discrete values. For a particle with spin quantum number s, the magnitude of its spin angular momentum is given by the formula S = √(s(s + 1))ℏ, where ℏ is the reduced Planck's constant.
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Percorso guidato
12:12
Conservation of Angular Momentum
Quantum Number
Quantum numbers are values that describe the quantized properties of particles in quantum mechanics. The spin quantum number, denoted as s, indicates the intrinsic angular momentum of a particle. For particles with spin s = 1, they can have three possible projections of spin along a chosen axis: +1, 0, and -1, which correspond to the allowed states of the particle.
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07:19Moles & Avogadro's Number
Reduced Planck's Constant (ℏ)
The reduced Planck's constant, denoted as ℏ (h-bar), is a fundamental constant in quantum mechanics, defined as ℏ = h/(2π), where h is the Planck constant. It plays a crucial role in quantifying angular momentum and other quantum properties. In the context of spin, it serves as a scaling factor that relates the quantum mechanical description of spin to classical angular momentum.
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08:59Phase Constant of a Wave Function
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