To determine which set of quantum numbers represents an electron in a hydrogen atom, we need to understand the quantum numbers and the electron configuration of hydrogen.
### Step-by-Step Solution:
1. **Identify the Electron Configuration of Hydrogen:**
- Hydrogen has one electron, and its electron configuration is \(1s^1\). This means that the electron is in the first energy level (n=1) and in the s subshell.
2. **Determine the Quantum Numbers:**
- The quantum numbers for an electron in a hydrogen atom can be defined as follows:
- **Principal Quantum Number (n)**: This represents the energy level of the electron. For hydrogen, since it has one electron in the first shell, \(n = 1\).
- **Azimuthal Quantum Number (l)**: This represents the subshell. For an s subshell, \(l = 0\).
- **Magnetic Quantum Number (m)**: This represents the orientation of the orbital. For \(l = 0\), the only possible value for \(m\) is \(0\).
- **Spin Quantum Number (s)**: This represents the spin of the electron. It can be either \(+\frac{1}{2}\) (spin up) or \(-\frac{1}{2}\) (spin down).
3. **Construct the Possible Sets of Quantum Numbers:**
- Based on the above information, the quantum numbers for the electron in hydrogen can be:
- For the first electron in the 1s orbital:
- Set 1: \( (n=1, l=0, m=0, s=+\frac{1}{2}) \)
- Set 2: \( (n=1, l=0, m=0, s=-\frac{1}{2}) \)
4. **Evaluate the Given Options:**
- Now, we need to compare the possible sets with the given options:
- Option 1: \( (1, 1, 0) \) - This is incorrect because \(l\) should be \(0\) for an s orbital.
- Option 2: \( (1, 0, 0, +\frac{1}{2}) \) - This is correct as it corresponds to the first electron in the 1s orbital.
- Option 3: \( (1, 0, 0, -\frac{1}{2}) \) - This is also a valid set for the second electron in the 1s orbital but is not listed as an option.
5. **Conclusion:**
- The correct set of quantum numbers that represents an electron in a hydrogen atom is Option 2: \( (1, 0, 0, +\frac{1}{2}) \).
