A hypothetical atom has energy levels given in the figure below. Which figure most accurately depicts the absorption spectrum, assuming all transitions between energy levels is possible? The black vertical lines represent the absorbed wavelengths.

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Chapter28: Atomic Physics
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### Absorption Spectrum and Energy Transitions in a Hypothetical Atom

A hypothetical atom has the following energy levels:

- Ground state: \( E_0 = -11.5 \, \text{eV} \)
- First excited state: \( E_1 = -9.6 \, \text{eV} \)
- Second excited state: \( E_2 = -5.2 \, \text{eV} \)
- Third excited state: \( E_3 = -1.1 \, \text{eV} \)

### Absorption Spectrum

The provided figure illustrates four potential absorption spectra, each represented by black vertical lines. These lines correspond to wavelengths of light absorbed by the atom as it transitions between different energy levels. 

The task is to determine which spectrum accurately represents all possible transitions between these energy levels. 

#### Explanation of Figures:

1. **First Figure**:
   - This spectrum has black vertical lines spread across it.
   - Wavelength increases from left to right.

2. **Second Figure**:
   - Another layout of black vertical lines.
   - Wavelength increases from left to right.

3. **Third Figure**:
   - Different arrangement of black vertical lines.
   - Wavelength increases from left to right.

4. **Fourth Figure**:
   - Yet another configuration of black vertical lines.
   - Wavelength increases from left to right.

### Determining the Correct Absorption Spectrum

To identify the correct absorption spectrum, consider the energy differences between the levels:

- \( E_0 \) to \( E_1 \): \( -9.6 \,\text{eV} - (-11.5 \, \text{eV}) = 1.9 \, \text{eV} \)
- \( E_0 \) to \( E_2 \): \( -5.2 \,\text{eV} - (-11.5 \, \text{eV}) = 6.3 \, \text{eV} \)
- \( E_0 \) to \( E_3 \): \( -1.1 \,\text{eV} - (-11.5 \, \text{eV}) = 10.4 \, \text{eV} \)
- \( E_1 \) to \( E_2 \): \( -5.2 \,\text{
Transcribed Image Text:### Absorption Spectrum and Energy Transitions in a Hypothetical Atom A hypothetical atom has the following energy levels: - Ground state: \( E_0 = -11.5 \, \text{eV} \) - First excited state: \( E_1 = -9.6 \, \text{eV} \) - Second excited state: \( E_2 = -5.2 \, \text{eV} \) - Third excited state: \( E_3 = -1.1 \, \text{eV} \) ### Absorption Spectrum The provided figure illustrates four potential absorption spectra, each represented by black vertical lines. These lines correspond to wavelengths of light absorbed by the atom as it transitions between different energy levels. The task is to determine which spectrum accurately represents all possible transitions between these energy levels. #### Explanation of Figures: 1. **First Figure**: - This spectrum has black vertical lines spread across it. - Wavelength increases from left to right. 2. **Second Figure**: - Another layout of black vertical lines. - Wavelength increases from left to right. 3. **Third Figure**: - Different arrangement of black vertical lines. - Wavelength increases from left to right. 4. **Fourth Figure**: - Yet another configuration of black vertical lines. - Wavelength increases from left to right. ### Determining the Correct Absorption Spectrum To identify the correct absorption spectrum, consider the energy differences between the levels: - \( E_0 \) to \( E_1 \): \( -9.6 \,\text{eV} - (-11.5 \, \text{eV}) = 1.9 \, \text{eV} \) - \( E_0 \) to \( E_2 \): \( -5.2 \,\text{eV} - (-11.5 \, \text{eV}) = 6.3 \, \text{eV} \) - \( E_0 \) to \( E_3 \): \( -1.1 \,\text{eV} - (-11.5 \, \text{eV}) = 10.4 \, \text{eV} \) - \( E_1 \) to \( E_2 \): \( -5.2 \,\text{
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