An electron in an atom has the following set of quantum numbers:
`n=3,l=2,m_(l)=+1,m_(s)=+1//2`
In which subshel can the electron be found?

Options

A. s
B. d
C. p
D. f

Answer

To determine the subshell in which the electron can be found based on the given quantum numbers \( n=3, l=2, m_l=+1, m_s=+\frac{1}{2} \), we can follow these steps:

### Step 1: Identify the Principal Quantum Number (n)
The principal quantum number \( n \) indicates the shell in which the electron resides. Here, \( n=3 \) means the electron is in the third shell.

### Step 2: Identify the Azimuthal Quantum Number (l)
The azimuthal quantum number \( l \) indicates the subshell type. The values of \( l \) correspond to different subshells:
- \( l=0 \) corresponds to the s subshell
- \( l=1 \) corresponds to the p subshell
- \( l=2 \) corresponds to the d subshell
- \( l=3 \) corresponds to the f subshell

In this case, since \( l=2 \), the electron is in the d subshell.

### Step 3: Identify the Magnetic Quantum Number (m_l)
The magnetic quantum number \( m_l \) indicates the orientation of the orbital within the subshell. For \( l=2 \) (d subshell), \( m_l \) can take values from \(-2\) to \(+2\) (i.e., -2, -1, 0, +1, +2). Here, \( m_l=+1 \) indicates one of the possible orientations of the d orbital.

### Step 4: Identify the Spin Quantum Number (m_s)
The spin quantum number \( m_s \) indicates the spin direction of the electron. The values can be \( +\frac{1}{2} \) (spin up) or \( -\frac{1}{2} \) (spin down). In this case, \( m_s=+\frac{1}{2} \) indicates that the electron has a spin in the upward direction.

### Conclusion
Based on the azimuthal quantum number \( l=2 \), we conclude that the electron is located in the **d subshell**.

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