Quantum Numbers worksheet for practicing electron configurations and quantum number notation.

To solve the problem, we need to fill in the electron configuration diagrams for the given elements (H, He, Li, and Be) using quantum numbers. Let's break it down step by step.

Quantum Numbers Recap:

1. Principal Quantum Number (\( n \)): Determines the energy level of the electron.
2. Azimuthal Quantum Number (\( l \)): Determines the subshell (s, p, d, f).
- \( l = 0 \) → s subshell
- \( l = 1 \) → p subshell
- \( l = 2 \) → d subshell
- \( l = 3 \) → f subshell
3. Magnetic Quantum Number (\( m_l \)): Determines the orbital within the subshell.
- For \( l = 0 \): \( m_l = 0 \)
- For \( l = 1 \): \( m_l = -1, 0, +1 \)
- For \( l = 2 \): \( m_l = -2, -1, 0, +1, +2 \)
- For \( l = 3 \): \( m_l = -3, -2, -1, 0, +1, +2, +3 \)
4. Spin Quantum Number (\( m_s \)): Determines the spin of the electron.
- \( m_s = +\frac{1}{2} \) or \( m_s = -\frac{1}{2} \)

Electron Configurations:

1. Hydrogen (H): Atomic number = 1
- Electron configuration: \( 1s^1 \)
- Only one electron in the \( 1s \) orbital.

2. Helium (He): Atomic number = 2
- Electron configuration: \( 1s^2 \)
- Two electrons in the \( 1s \) orbital.

3. Lithium (Li): Atomic number = 3
- Electron configuration: \( 1s^2 2s^1 \)
- Two electrons in the \( 1s \) orbital and one electron in the \( 2s \) orbital.

4. Beryllium (Be): Atomic number = 4
- Electron configuration: \( 1s^2 2s^2 \)
- Two electrons in the \( 1s \) orbital and two electrons in the \( 2s \) orbital.

Filling the Diagrams:

#### 1. Hydrogen (H)
- 1s:
- \( n = 1 \), \( l = 0 \), \( m_l = 0 \), \( m_s = +\frac{1}{2} \)
- One electron in the \( 1s \) orbital.

| Orbital Designation | \( n \) | \( l \) | \( m_l \) | \( m_s \) |
|---------------------|---------|---------|-----------|-----------|
| \( 1s \) | 1 | 0 | 0 | \( +\frac{1}{2} \) |

#### 2. Helium (He)
- 1s:
- \( n = 1 \), \( l = 0 \), \( m_l = 0 \), \( m_s = +\frac{1}{2} \) and \( m_s = -\frac{1}{2} \)
- Two electrons in the \( 1s \) orbital.

| Orbital Designation | \( n \) | \( l \) | \( m_l \) | \( m_s \) |
|---------------------|---------|---------|-----------|-----------|
| \( 1s \) | 1 | 0 | 0 | \( +\frac{1}{2} \) |
| \( 1s \) | 1 | 0 | 0 | \( -\frac{1}{2} \) |

#### 3. Lithium (Li)
- 1s:
- \( n = 1 \), \( l = 0 \), \( m_l = 0 \), \( m_s = +\frac{1}{2} \) and \( m_s = -\frac{1}{2} \)
- Two electrons in the \( 1s \) orbital.
- 2s:
- \( n = 2 \), \( l = 0 \), \( m_l = 0 \), \( m_s = +\frac{1}{2} \)
- One electron in the \( 2s \) orbital.

| Orbital Designation | \( n \) | \( l \) | \( m_l \) | \( m_s \) |
|---------------------|---------|---------|-----------|-----------|
| \( 1s \) | 1 | 0 | 0 | \( +\frac{1}{2} \) |
| \( 1s \) | 1 | 0 | 0 | \( -\frac{1}{2} \) |
| \( 2s \) | 2 | 0 | 0 | \( +\frac{1}{2} \) |

#### 4. Beryllium (Be)
- 1s:
- \( n = 1 \), \( l = 0 \), \( m_l = 0 \), \( m_s = +\frac{1}{2} \) and \( m_s = -\frac{1}{2} \)
- Two electrons in the \( 1s \) orbital.
- 2s:
- \( n = 2 \), \( l = 0 \), \( m_l = 0 \), \( m_s = +\frac{1}{2} \) and \( m_s = -\frac{1}{2} \)
- Two electrons in the \( 2s \) orbital.

| Orbital Designation | \( n \) | \( l \) | \( m_l \) | \( m_s \) |
|---------------------|---------|---------|-----------|-----------|
| \( 1s \) | 1 | 0 | 0 | \( +\frac{1}{2} \) |
| \( 1s \) | 1 | 0 | 0 | \( -\frac{1}{2} \) |
| \( 2s \) | 2 | 0 | 0 | \( +\frac{1}{2} \) |
| \( 2s \) | 2 | 0 | 0 | \( -\frac{1}{2} \) |

Final Answer:

\[
\boxed{
\begin{array}{c|c|c|c|c}
\text{Orbital Designation} & n & l & m_l & m_s \\
\hline
\text{H: } 1s & 1 & 0 & 0 & +\frac{1}{2} \\
\hline
\text{He: } 1s & 1 & 0 & 0 & +\frac{1}{2} \\
\text{He: } 1s & 1 & 0 & 0 & -\frac{1}{2} \\
\hline
\text{Li: } 1s & 1 & 0 & 0 & +\frac{1}{2} \\
\text{Li: } 1s & 1 & 0 & 0 & -\frac{1}{2} \\
\text{Li: } 2s & 2 & 0 & 0 & +\frac{1}{2} \\
\hline
\text{Be: } 1s & 1 & 0 & 0 & +\frac{1}{2} \\
\text{Be: } 1s & 1 & 0 & 0 & -\frac{1}{2} \\
\text{Be: } 2s & 2 & 0 & 0 & +\frac{1}{2} \\
\text{Be: } 2s & 2 & 0 & 0 & -\frac{1}{2} \\
\end{array}
}
\]