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Chapter 5: Problem 3

Suppose an atom has three energy levels, specified in arbitrary units as \(10,7,\) and \(5 .\) In these units, which of the following energies might an emitted photon have? (Select all that apply.) a. 3 b. 2 c. 5 d. 4

Short Answer

Expert verified
The correct photon energies are 3, 2, and 5. Thus, the correct options are a, b, and c.

Step by step solution

01

Determine Possible Energy Differences

Calculate the energy differences between the given energy levels to find the possible photon energies that can be emitted. The energy levels given are 10, 7, and 5.
02

Calculate Difference Between Levels 10 and 7

The energy difference between the energy levels 10 and 7 is calculated as:\( 10 - 7 = 3 \ \)
03

Calculate Differences Between Levels 10 and 5

The energy difference between the energy levels 10 and 5 is calculated as:\( 10 - 5 = 5 \ \)
04

Calculate Difference Between Levels 7 and 5

The energy difference between the energy levels 7 and 5 is calculated as:\( 7 - 5 = 2 \ \)
05

Identify Possible Photon Energies

From the previous steps, the possible photon energies that might be emitted are 3, 5, and 2 units.
06

Compare with Given Options

Compare the calculated possible photon energies (3, 2, 5) with the options provided: a. 3, b. 2, c. 5, d. 4.
07

Determine the Correct Answers

The energies that match the calculated values are 3, 2, and 5. Therefore, the correct answers are options a, b, and c.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

atomic energy levels
Atoms consist of a nucleus surrounded by electrons that exist in specific energy levels. Each energy level corresponds to a different amount of energy. When electrons move between these levels, energy is either absorbed or emitted. Understanding these levels is crucial for understanding various phenomena in chemistry and physics.
Energy levels are often labeled with numbers or letters. Higher numbers correspond to higher energy states. In our example, the energy levels are 10, 7, and 5. The difference in energy between these levels plays a significant role in photon emission.
photon emission
Photons are particles of light that carry energy. When an electron in an atom jumps from a higher energy level to a lower one, it emits a photon. The energy of the emitted photon equals the difference in energy between the two levels.
This process can be visualized as a drop or jump between energy levels. The bigger the gap between levels, the more energetic the emitted photon will be.
  • If the electron moves from 10 to 7, it emits a photon with an energy of 3 units.
  • If it moves from 10 to 5, it emits a photon with an energy of 5 units.
  • If it moves from 7 to 5, it emits a photon with an energy of 2 units.
energy difference calculation
Calculating the energy difference between atomic energy levels is essential to determining the energy of emitted photons. The difference is simply the subtraction of the lower energy level from the higher one.
For the given energy levels (10, 7, and 5), you perform the following calculations:
  1. Energy difference between 10 and 7: 10 - 7 = 3
  2. Energy difference between 10 and 5: 10 - 5 = 5
  3. Energy difference between 7 and 5: 7 - 5 = 2
These calculations tell us the possible energies of the emitted photons. By comparing with given options, we find the correct answers: 3, 5, and 2 units are the possible photon energies.

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