Question

The magnetic quantum number for d-orbital is given by

• A. 2
• B. 0, \(\pm1\), \(\pm2\)
• C. 0, 1, 2
• D. 5

Hint:

Number of orbitals = 2l+1; for d-orbitals (l=2), there are 5 orbitals.

Answer 1

The Correct Option is B

To determine the magnetic quantum number for the d-orbital, we need to understand the quantum number system in quantum mechanics, which describes the properties of atomic orbitals and electrons in an atom.

The four quantum numbers are: 

• Principal quantum number (\(n\)): Indicates the main energy level or shell of an electron.
• Angular momentum quantum number (\(l\)): Determines the shape of the orbital. For d-orbitals, \(l = 2\).
• Magnetic quantum number (\(m_l\)): Specifies the orientation of the orbital in space. It takes values from \(-l\) to \(+l\), including zero.
• Spin quantum number: Refers to the spin of the electron, which can be either \(+\frac{1}{2}\) or \(-\frac{1}{2}\).

For d-orbitals, where the angular momentum quantum number \(l\) is 2, the possible values for the magnetic quantum number \(m_{l}\) can be calculated as:

\(l\)	\(m_l\) Values
2	0, \(\pm1\), \(\pm2\)

The range of \(m_{l}\) is determined by the values between \(-l\) and \(+l\) (inclusive), which results in the sequence \({0, \pm1, \pm2}\). Therefore, the correct answer is 0, \(\pm1\), \(\pm2\).

In conclusion, the magnetic quantum number for the d-orbital includes five possible values: 0, ±1, and ±2, which corresponds to the various orientations of the d-orbitals in an atom.