Textbook Question
The energy of the state of lithium is eV. Calculate the value of for this state.
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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 33b
Young & Freedman Calc 14th EditionCh 41: Quantum Mechanics II: Atomic StructureProblem 33bChapter 41, Problem 33b
Estimate the energy of the least strongly bound level in the shell of N2+.
Verified step by step guidance1
Step 1: Understand the problem. The question asks for the energy of the least strongly bound level in the L shell of N2+. This involves calculating the binding energy of an electron in the L shell of a nitrogen ion with a charge of +2.
Step 2: Recall the formula for the energy levels of a hydrogen-like ion: \( E_n = - \frac{Z^2 \cdot R_H}{n^2} \), where \( Z \) is the atomic number, \( R_H \) is the Rydberg constant, and \( n \) is the principal quantum number. For the L shell, \( n = 2 \).
Step 3: Determine the effective nuclear charge \( Z_{eff} \). For N2+, the atomic number \( Z \) of nitrogen is 7, but since two electrons have been removed, the effective nuclear charge experienced by the remaining electrons will be higher due to reduced electron shielding.
Step 4: Substitute \( Z_{eff} \), \( R_H \), and \( n = 2 \) into the formula \( E_n = - \frac{Z_{eff}^2 \cdot R_H}{n^2} \). This will give the energy of the least strongly bound level in the L shell.
Step 5: Interpret the result. The negative sign in the energy indicates that the electron is bound to the nucleus. The magnitude of the energy represents how strongly the electron is bound, with smaller absolute values corresponding to less strongly bound levels.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Binding Energy
Binding energy is the energy required to remove an electron from an atom or ion. In the context of atomic physics, it indicates how strongly an electron is held by the nucleus. The least strongly bound level corresponds to the electron that is easiest to remove, which is crucial for understanding ionization processes and energy levels in multi-electron systems.
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Quantum Levels
Quantum levels, or energy levels, refer to the discrete energy states that electrons can occupy in an atom. Each level is associated with a specific quantum number and can hold a limited number of electrons. For nitrogen ions like N2+, the L shell corresponds to the second energy level, which is important for determining the energy of electrons in that shell.
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Ionization Energy
Ionization energy is the amount of energy needed to remove an electron from an atom or ion in its gaseous state. It is a critical concept in understanding the stability of electrons in various shells and how they interact with external energy sources. For N2+, estimating the energy of the least strongly bound level involves calculating the ionization energy for the L shell electrons.
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Related Practice
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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Textbook Question
The electron in rubidium (Rb) sees an effective charge of . Calculate the ionization energy of this electron.
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Textbook Question
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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Textbook Question
The energies for an electron in the , , and shells of the tungsten atom are eV, eV, and eV, respectively. Calculate the wavelengths of the and x rays of tungsten.
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Textbook Question
Estimate the energy of the highest- state for (a) the shell of Be+ and (b) the shell of Ca+.
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