Ch 38: Quantization

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 38: Quantization

Problem 27a

Chapter 38, Problem 27a

The allowed energies of a simple atom are 0.00 eV, 4.00 eV, and 6.00 eV. Draw the atom’s energy-level diagram. Label each level with the energy and the quantum number.

Verified step by step guidance

Step 1: Understand the concept of energy levels in an atom. Energy levels represent the discrete energies that electrons in an atom can occupy. Each energy level is associated with a quantum number, typically denoted as n.

Step 2: Identify the given energy levels from the problem. The allowed energies are 0.00 eV, 4.00 eV, and 6.00 eV. These correspond to different quantum states of the atom.

Step 3: Assign quantum numbers to each energy level. Typically, the lowest energy level (ground state) is assigned n = 1, the next higher energy level is n = 2, and so on. For this atom: 0.00 eV corresponds to n = 1, 4.00 eV corresponds to n = 2, and 6.00 eV corresponds to n = 3.

Step 4: Draw the energy-level diagram. Represent the energy levels as horizontal lines on a vertical axis, where the vertical axis represents energy (in eV). Label each line with its corresponding energy value and quantum number. For example: the line at 0.00 eV is labeled 'n = 1, 0.00 eV', the line at 4.00 eV is labeled 'n = 2, 4.00 eV', and the line at 6.00 eV is labeled 'n = 3, 6.00 eV'.

Step 5: Ensure the diagram is clear and properly scaled. The spacing between the energy levels should reflect the difference in energy values (e.g., the gap between 0.00 eV and 4.00 eV should be smaller than the gap between 4.00 eV and 6.00 eV). This helps visually represent the relative energy differences.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Energy Levels

Energy levels in an atom represent the specific energies that electrons can have. These levels are quantized, meaning electrons can only occupy certain discrete energy states, which are often denoted by quantum numbers. In this case, the allowed energies of 0.00 eV, 4.00 eV, and 6.00 eV indicate the possible states an electron can occupy in the atom.

Quantum Numbers

Quantum numbers are numerical values that describe the unique quantum state of an electron in an atom. The principal quantum number (n) indicates the energy level, while other quantum numbers (like angular momentum and magnetic quantum numbers) provide additional information about the electron's position and behavior. For the given energy levels, each energy can be associated with a specific quantum number.

Energy-Level Diagram

An energy-level diagram visually represents the allowed energy levels of an atom, typically arranged vertically with increasing energy. Each level is labeled with its corresponding energy value and quantum number. This diagram helps illustrate the concept of quantization in atomic physics, showing how electrons can transition between these levels by absorbing or emitting energy.

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