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

Options

A. Potential energy increases and kinetic energy decreases
B. Kinetic energy increases and potential energy decreases
C. Both KE and PE increases
D. Both KE and PE decreases

Answer

To solve the question regarding the changes in potential energy and kinetic energy when a hydrogen atom is raised from the ground state to an excited state, we can follow these steps:

### Step 1: Understand the System
A hydrogen atom consists of a single electron revolving around a nucleus (proton). The electron can occupy different energy levels, with the ground state being the lowest energy level.

**Hint:** Remember that the ground state corresponds to the lowest energy configuration of the atom.

### Step 2: Identify Forces Acting on the Electron
The centripetal force required for the electron to revolve around the nucleus is provided by the electrostatic force of attraction between the negatively charged electron and the positively charged proton.

**Hint:** Recall Coulomb's law for the electrostatic force between two charges.

### Step 3: Write the Expressions for Kinetic and Potential Energy
- The kinetic energy (KE) of the electron can be expressed as:
\[ KE = \frac{1}{2} mv^2 \]
- The potential energy (PE) of the electron in the electric field of the proton is given by:
\[ PE = -\frac{k \cdot e^2}{r} \]
where \( k \) is Coulomb's constant, \( e \) is the charge of the electron, and \( r \) is the radius of the orbit.

**Hint:** Remember that potential energy is negative in this context due to the attractive nature of the force.

### Step 4: Analyze the Changes in Energy States
When the electron is excited to a higher energy level:
- The radius \( r \) of the orbit increases.
- As the radius increases, the kinetic energy decreases because the electron moves slower in a higher orbit (further from the nucleus).

**Hint:** Consider how the radius affects the speed of the electron and the centripetal force balance.

### Step 5: Analyze the Potential Energy Change
As the radius increases, the potential energy becomes less negative (increases in magnitude) because:
\[ PE \text{ increases as } r \text{ increases.} \]
Thus, the overall potential energy increases (becomes less negative).

**Hint:** Think about how moving further away from the nucleus affects the potential energy in a bound system.

### Step 6: Conclusion
- **Kinetic Energy (KE)**: Decreases when the electron moves to a higher energy state.
- **Potential Energy (PE)**: Increases (becomes less negative) when the electron moves to a higher energy state.

Thus, when a hydrogen atom is raised from the ground state to an excited state, the potential energy increases and the kinetic energy decreases.

**Final Answer:** Potential energy increases, kinetic energy decreases.

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