which cation cannot be identified by flame test ?

Options

A. `Na^(+)`
B. `K^(+)`
C. `Ba^(2+)`
D. `Mg^(2+)`

Explanation

To determine which cation cannot be identified by a flame test, we will analyze the options provided: Na\(^+\), K\(^+\), Ba\(^{2+}\), and Mg\(^{2+}\).

### Step-by-Step Solution:

1. **Understanding Flame Test**:
- The flame test is a qualitative analysis technique used to identify the presence of certain metal ions based on the color they emit when heated in a flame. The color emitted is due to the excitation of electrons in the metal ions.

2. **Analyzing Sodium (Na\(^+\))**:
- Sodium has an electronic configuration of 1s\(^2\) 2s\(^2\) 2p\(^6\) 3s\(^1\).
- The outermost electron is in the 3rd shell (3s), which can be easily excited to a higher energy level.
- **Conclusion**: Sodium can be identified by flame test (emits a bright yellow color).

3. **Analyzing Potassium (K\(^+\))**:
- Potassium has an electronic configuration of 1s\(^2\) 2s\(^2\) 2p\(^6\) 3s\(^2\) 3p\(^6\) 4s\(^1\).
- The outermost electron is in the 4th shell (4s), which can also be easily excited.
- **Conclusion**: Potassium can be identified by flame test (emits a lilac color).

4. **Analyzing Barium (Ba\(^{2+}\))**:
- Barium has an electronic configuration of 1s\(^2\) 2s\(^2\) 2p\(^6\) 3s\(^2\) 3p\(^6\) 4s\(^2\) 4p\(^6\) 5s\(^2\) 5p\(^6\) 6s\(^2\).
- The outermost electrons are in the 6th shell (6s), which can be excited with sufficient energy.
- **Conclusion**: Barium can be identified by flame test (emits a green color).

5. **Analyzing Magnesium (Mg\(^{2+}\))**:
- Magnesium has an electronic configuration of 1s\(^2\) 2s\(^2\) 2p\(^6\) 3s\(^2\).
- The outermost electrons are in the 3rd shell (3s). However, magnesium's atomic size is smaller compared to sodium, making it more difficult to excite its electrons.
- **Conclusion**: Magnesium cannot be effectively identified by flame test as it requires higher energy to excite its electrons.

### Final Answer:
The cation that cannot be identified by flame test is **Mg\(^{2+}\)**.

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