Values of magnetic orbital quantum for an electron of M-shell can be:

Options

A. 0,1,2
B. `-2,-1,0,+1,+2`
C. `0,1,2,3`
D. `-1,0,+1`

Answer

To determine the possible values of the magnetic orbital quantum number (m_l) for an electron in the M-shell, we need to follow these steps:

### Step 1: Identify the Principal Quantum Number (n)
The M-shell corresponds to the principal quantum number \( n = 3 \).

### Step 2: Determine the Possible Values of the Azimuthal Quantum Number (l)
For a given principal quantum number \( n \), the azimuthal quantum number \( l \) can take values from \( 0 \) to \( n-1 \). Therefore, for \( n = 3 \):
- The possible values of \( l \) are:
- \( l = 0 \) (s orbital)
- \( l = 1 \) (p orbital)
- \( l = 2 \) (d orbital)

### Step 3: Determine the Possible Values of the Magnetic Orbital Quantum Number (m_l)
The magnetic orbital quantum number \( m_l \) can take values from \( -l \) to \( +l \), including zero. Thus, we calculate the possible values of \( m_l \) for each value of \( l \):
- For \( l = 0 \):
- \( m_l = 0 \)
- For \( l = 1 \):
- \( m_l = -1, 0, +1 \)
- For \( l = 2 \):
- \( m_l = -2, -1, 0, +1, +2 \)

### Step 4: Combine All Possible Values of m_l
Now we combine all the possible values of \( m_l \) from the above calculations:
- From \( l = 0 \): \( 0 \)
- From \( l = 1 \): \( -1, 0, +1 \)
- From \( l = 2 \): \( -2, -1, 0, +1, +2 \)

Thus, the complete set of possible values for \( m_l \) is:
- \( -2, -1, 0, +1, +2 \)

### Final Answer
The values of the magnetic orbital quantum number for an electron of the M-shell can be: \( -2, -1, 0, +1, +2 \).

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