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 Calc15th EditionUniversity PhysicsISBN: 9780135159552
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors37
- Ch 02: Motion Along a Straight Line57
- Ch 03: Motion in Two or Three Dimensions45
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws54
- Ch 06: Work & Kinetic Energy11
- Ch 07: Potential Energy & Conservation6
- Ch 08: Momentum, Impulse, and Collisions15
- Ch 09: Rotation of Rigid Bodies37
- Ch 10: Dynamics of Rotational Motion44
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics27
- Ch 13: Gravitation34
- Ch 14: Periodic Motion26
- Ch 15: Mechanical Waves22
- Ch 16: Sound & Hearing28
- Ch 17: Temperature and Heat28
- Ch 18: Thermal Properties of Matter35
- Ch 19: The First Law of Thermodynamics29
- Ch 20: The Second Law of Thermodynamics18
- Ch 21: Electric Charge and Electric Field28
- Ch 22: Gauss' Law21
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF24
- Ch 26: Direct-Current Circuits29
- Ch 27: Magnetic Field and Magnetic Forces16
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction22
- Ch 30: Inductance14
- Ch 31: Alternating Current20
- Ch 33: The Nature and Propagation of Light17
- Ch 34: Geometric Optics29
- Ch 35: Interference13
- Ch 36: Diffraction19
- Ch 37: Special Relativity19
- Ch 38: Photons: Light Waves Behaving as Particles12
- Ch 39: Particles Behaving as Waves25
- Ch 40: Quantum Mechanics I: Wave Functions20
- Ch 41: Quantum Mechanics II: Atomic Structure21
- Ch 42: Molecules and Condensed Matter17
- Ch 43: Nuclear Physics13
- Ch 44: Particle Physics and Cosmology17
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
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Young & Freedman Calc 15th EditionCh 41: Quantum Mechanics II: Atomic StructureProblem 35b
Young & Freedman Calc 15th EditionCh 41: Quantum Mechanics II: Atomic StructureProblem 35bChapter 40, Problem 35b
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 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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