Textbook Question
The energies of the , , and states of potassium are given in Example . Calculate for each state. What trend do your results show? How can you explain this trend?
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Ch 41: Quantum Mechanics II: Atomic Structure
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors41
- Ch 02: Motion Along a Straight Line67
- Ch 03: Motion in Two or Three Dimensions47
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws59
- Ch 06: Work & Kinetic Energy14
- Ch 07: Potential Energy & Conservation8
- Ch 08: Momentum, Impulse, and Collisions18
- Ch 09: Rotation of Rigid Bodies42
- Ch 10: Dynamics of Rotational Motion48
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics31
- Ch 13: Gravitation35
- Ch 14: Periodic Motion32
- Ch 15: Mechanical Waves25
- Ch 16: Sound & Hearing32
- Ch 17: Temperature and Heat36
- Ch 18: Thermal Properties of Matter38
- Ch 19: The First Law of Thermodynamics33
- Ch 20: The Second Law of Thermodynamics22
- Ch 21: Electric Charge and Electric Field36
- Ch 22: Gauss' Law24
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF26
- Ch 26: Direct-Current Circuits30
- Ch 27: Magnetic Field and Magnetic Forces18
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction28
- Ch 30: Inductance17
- Ch 31: Alternating Current21
- Ch 32: Electromagnetic Waves1
- Ch 33: The Nature and Propagation of Light20
- Ch 34: Geometric Optics34
- Ch 35: Interference19
- Ch 36: Diffraction25
- Ch 37: Special Relativity20
- Ch 38: Photons: Light Waves Behaving as Particles15
- Ch 39: Particles Behaving as Waves26
- Ch 40: Quantum Mechanics I: Wave Functions21
- Ch 41: Quantum Mechanics II: Atomic Structure25
- Ch 42: Molecules and Condensed Matter18
- Ch 43: Nuclear Physics16
- Ch 44: Particle Physics and Cosmology23
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
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Young & Freedman Calc 14th EditionCh 41: Quantum Mechanics II: Atomic StructureProblem 34a
Young & Freedman Calc 14th EditionCh 41: Quantum Mechanics II: Atomic StructureProblem 34aChapter 41, Problem 34a
The energy of the state of lithium is eV. Calculate the value of for this state.
Verified step by step guidance1
Understand the concept of effective nuclear charge (Zeff): Zeff is the net positive charge experienced by an electron in a multi-electron atom. It accounts for the shielding effect caused by other electrons.
Use the formula for the energy of an electron in a hydrogen-like atom: \( E_n = -13.6 \frac{Z_{\text{eff}}^2}{n^2} \) (in eV), where \( E_n \) is the energy of the electron, \( Z_{\text{eff}} \) is the effective nuclear charge, and \( n \) is the principal quantum number.
Rearrange the formula to solve for \( Z_{\text{eff}} \): \( Z_{\text{eff}} = \sqrt{\frac{-E_n \cdot n^2}{13.6}} \).
Substitute the given values into the formula: \( E_n = -5.391 \ \text{eV} \) and \( n = 2 \) (since the electron is in the 2s state).
Simplify the expression to calculate \( Z_{\text{eff}} \): Perform the square root and division operations to find the effective nuclear charge for the 2s state of lithium.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Effective Nuclear Charge (Zeff)
Effective Nuclear Charge (Zeff) is the net positive charge experienced by an electron in a multi-electron atom. It accounts for the shielding effect caused by other electrons, which reduces the full nuclear charge. Zeff can be calculated using the formula Zeff = Z - S, where Z is the atomic number and S is the shielding constant. Understanding Zeff is crucial for predicting electron behavior and energy levels in atoms.
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Energy Levels in Atoms
Energy levels in atoms refer to the quantized states that electrons can occupy. Each energy level corresponds to a specific energy value, which is influenced by the nuclear charge and electron-electron interactions. The energy of an electron in a given state can be calculated using the formula E = -Zeff^2 * 13.6 eV/n^2, where n is the principal quantum number. This concept is essential for understanding electron configurations and transitions.
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Quantum Mechanics and Electron States
Quantum mechanics describes the behavior of particles at atomic and subatomic levels, including electrons in atoms. It introduces the idea that electrons exist in discrete states or orbitals, each with specific energy levels. The principles of quantum mechanics, such as wave-particle duality and uncertainty, are fundamental for analyzing electron configurations and predicting the properties of elements, including their ionization energies.
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The doubly charged ion N2+ is formed by removing two electrons from a nitrogen atom. What is the ground-state electron configuration for the N2+ ion?
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Estimate the energy of the least strongly bound level in the shell of N2+.
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Estimate the energy of the highest- state for (a) the shell of Be+ and (b) the shell of Ca+.
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