An atom consists of theree energy levels given by a ground state with energy `E_(0)=0`, the first excited state with energy `E_(1)=K` and the second excited state with energy `E_(2)=2K` where `K gt 0`. The atom is initially in the ground state. Light from a laser which emits photons with energy `1.5 K` is shined on the atom. Which of the following is`//`are correct?

Options

A. The photons are absorbed, putting one atom in a state `E_(1)` and one atom in a state `E_(2)`
B. A photon will always be absorbed, but half the time the atom will go into the state with energy K and the other half into state with energy 2K. In this way, energy will be conserved on the average
C. The atom absorbs a photon, goes into the the first excited state with energy K and emits a photon with energy 0.5 K to conserve energy
D. The atom does not absorb any photon and stays in the ground state.

Explanation

To solve the problem, we need to analyze the energy levels of the atom and the energy of the incoming photon from the laser.

### Step-by-Step Solution:

1. **Identify the Energy Levels**:
- Ground state energy, \( E_0 = 0 \)
- First excited state energy, \( E_1 = K \)
- Second excited state energy, \( E_2 = 2K \)

2. **Photon Energy**:
- The energy of the photon emitted by the laser is \( E_{\text{photon}} = 1.5K \).

3. **Determine Possible Transitions**:
- The atom is initially in the ground state \( E_0 \).
- The atom can absorb a photon and transition to a higher energy state if the energy of the photon matches the energy difference between the current state and the target state.
- Possible transitions from the ground state:
- To the first excited state: \( E_1 - E_0 = K - 0 = K \)
- To the second excited state: \( E_2 - E_0 = 2K - 0 = 2K \)

4. **Compare Photon Energy with Energy Differences**:
- The energy of the photon \( 1.5K \) does not match either \( K \) or \( 2K \).
- Therefore, the atom cannot absorb the photon to transition to either excited state directly.

5. **Conclusion**:
- Since the photon energy does not correspond to any of the energy differences available for transitions from the ground state, the atom cannot absorb the photon and will remain in the ground state.

### Final Answer:
The correct conclusion is that the atom does not absorb any photon and stays in the ground state.

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