**Category:** Quantum Mechanics  
**Subtype:** Atomic Transitions  
**Problem Description:** This problem involves the energy changes of an atom as it transitions between two energy levels. Specifically, it asks whether the atom absorbs or emits a photon when moving from a higher energy state (\(E_n\)) to a lower energy state (\(E_m\)), and what the energy of that photon is.  

**Key Concepts:**  
- When an atom transitions from a higher energy level to a lower one, it emits a photon.  
- The energy of the emitted photon is equal to the difference in energy between the two levels.  

**Answer Options Analysis:**  
- **A:** Incorrect - Absorption occurs when moving to a higher energy state.  
- **B:** Correct - The atom emits a photon with energy equal to \(E_m - E_n\) (which is negative, indicating energy loss).  
- **C:** Incorrect - This option incorrectly states the energy difference.  
- **D:** Incorrect - This option describes absorption, which is not applicable here.  

**Conclusion:** The correct answer is **B**.