When a hydrogen atom is raised from the ground state to an excited state

Options

A. Both K.E and P.E increase
B. Both K.E and P.E, decrease
C. The P.E decreases and K.E increases
D. The P.E increases and K.E. Decreases

Answer

To solve the question regarding the behavior of a hydrogen atom when it is raised from the ground state to an excited state, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Initial and Final States**:
- The hydrogen atom starts in the ground state, which corresponds to the principal quantum number \( n = 1 \).
- When the atom is excited, it moves to a higher energy level, which corresponds to \( n > 1 \).

2. **Understand the Relationship of Radius and Principal Quantum Number**:
- The radius of the electron's orbit in a hydrogen atom is given by the formula:
\[ r_n = a_0 n^2 \]
where \( a_0 \) is the Bohr radius (approximately \( 5.29 \times 10^{-11} \) m).
- As \( n \) increases, the radius \( r_n \) also increases.

3. **Kinetic Energy Calculation**:
- The kinetic energy \( K \) of the electron in a hydrogen atom can be expressed as:
\[ K = \frac{Z e^2}{2r} \]
For hydrogen, \( Z = 1 \), so:
\[ K = \frac{e^2}{2r} \]
- Since the radius \( r \) increases when moving to a higher energy state (higher \( n \)), the kinetic energy \( K \) will decrease.

4. **Potential Energy Calculation**:
- The potential energy \( U \) of the electron in a hydrogen atom is given by:
\[ U = -\frac{K e^2}{r} \]
- As the radius \( r \) increases, the potential energy becomes less negative (i.e., it increases). For example, moving from \( -13.6 \, \text{eV} \) (ground state) to \( -3.4 \, \text{eV} \) (first excited state) shows an increase in potential energy.

5. **Conclusion**:
- When a hydrogen atom is excited from the ground state to an excited state:
- The radius increases.
- The kinetic energy decreases.
- The potential energy increases (becomes less negative).
- Therefore, the correct conclusion is that as the atom transitions from the ground state to an excited state, the kinetic energy decreases while the potential energy increases.

### Final Answer:
The correct option is that the kinetic energy decreases and the potential energy increases when a hydrogen atom is raised from the ground state to an excited state.

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