Question

The orbital which contain the electron with the following set of four quantum numbers \[ n=2,\ l=0,\ m_l=0,\ m_s=-\frac{1}{2} \] is ____.

• A. \(1s\)
• B. \(2s\)
• C. \(2p\)
• D. \(2d\)

Hint:

Remember the relation between \(l\) and orbitals:
• \(l=0 \rightarrow s\)
• \(l=1 \rightarrow p\)
• \(l=2 \rightarrow d\)
• \(l=3 \rightarrow f\)

Answer 1

The Correct Option is B

Concept:
Quantum numbers describe the complete position and nature of an electron inside an atom. The four quantum numbers are:
• Principal quantum number (\(n\))
• Angular momentum quantum number (\(l\))
• Magnetic quantum number (\(m_l\))
• Spin quantum number (\(m_s\)) Each quantum number gives specific information about the electron.

Step 1: Interpret the principal quantum number \(n\).
Given: \[ n=2 \] This means the electron belongs to the: \[ \text{Second energy shell} \] Possible orbitals in second shell are: \[ 2s,\ 2p \]

Step 2: Interpret the azimuthal quantum number \(l\).
Given: \[ l=0 \] Values of \(l\) correspond to orbitals as: \[ l=0 \rightarrow s \] \[ l=1 \rightarrow p \] \[ l=2 \rightarrow d \] Since: \[ l=0 \] the orbital must be an: \[ s \text{ orbital} \]

Step 3: Use the value of \(n\) together with \(l\).
We already know:
• \(n=2\)
• \(l=0\) Therefore the orbital is: \[ \boxed{2s} \]

Step 4: Check remaining quantum numbers.
For an \(s\)-orbital: \[ m_l = 0 \] which matches the given value. The spin quantum number: \[ m_s = -\frac{1}{2} \] only tells the spin direction and does not change the orbital type.

Step 5: Select the correct option.
Thus, the electron belongs to: \[ \boxed{2s} \] Hence, \[ \boxed{(2)\ 2s} \]