1a) Use the table below to determine the energy in eV of the photon absorbed when an electron jumps up from the n = 1 orbit to the n = 2 orbit of a hydrogen atom.  =_________ eV 1b ) Use the table shown below to determine the energy in eV of the photon emitted when an electron jumps down from the n = 3 orbit to the n = 2 orbit of a hydrogen atom. =___________ eV

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1a) Use the table below to determine the energy in eV of the photon absorbed when an electron jumps up from the n = 1 orbit to the n = 2 orbit of a hydrogen atom.
 =_________ eV

1b ) Use the table shown below to determine the energy in eV of the photon emitted when an electron jumps down from the n = 3 orbit to the n = 2 orbit of a hydrogen atom.
=___________ eV

 
**Allowed Values of the Hydrogen Electron's Radius and Energy for Low Values of n**

This table provides the permitted values for the radius and energy of a hydrogen electron for low quantum numbers, denoted as \( n \).

| \( n \) | \( r_n \) (radius in nm) | \( E_n \) (energy in eV) |
|-------|-------------------------|-------------------------|
| 1     | 0.053 nm                             | \(-13.60\) eV                   |
| 2     | 0.212 nm                           | \(-3.40\) eV                     |
| 3     | 0.477 nm                           | \(-1.51\) eV                     |
| 4     | 0.848 nm                           | \(-0.85\) eV                    |

**Explanation:**

- **Columns**:
  - **n**: Indicates the principal quantum number, which denotes the electron's energy level in a hydrogen atom.
  - **\( r_n \)**: Represents the radius of the electron's orbit in nanometers (nm).
  - **\( E_n \)**: Shows the energy of the electron in electron volts (eV), with negative values indicating bound states.

As \( n \) increases, the radius \( r_n \) increases, and the energy \( E_n \) approaches zero from negative values, showing that electrons at higher energy levels are less tightly bound.
Transcribed Image Text:**Allowed Values of the Hydrogen Electron's Radius and Energy for Low Values of n** This table provides the permitted values for the radius and energy of a hydrogen electron for low quantum numbers, denoted as \( n \). | \( n \) | \( r_n \) (radius in nm) | \( E_n \) (energy in eV) | |-------|-------------------------|-------------------------| | 1 | 0.053 nm | \(-13.60\) eV | | 2 | 0.212 nm | \(-3.40\) eV | | 3 | 0.477 nm | \(-1.51\) eV | | 4 | 0.848 nm | \(-0.85\) eV | **Explanation:** - **Columns**: - **n**: Indicates the principal quantum number, which denotes the electron's energy level in a hydrogen atom. - **\( r_n \)**: Represents the radius of the electron's orbit in nanometers (nm). - **\( E_n \)**: Shows the energy of the electron in electron volts (eV), with negative values indicating bound states. As \( n \) increases, the radius \( r_n \) increases, and the energy \( E_n \) approaches zero from negative values, showing that electrons at higher energy levels are less tightly bound.
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