Orbital angular momentum depends on.........

Explanation:

The orbital angular momentum of an electron in an atom is determined by the azimuthal quantum number (l). This quantum number defines the shape of the electron's orbital and its angular momentum. The principal quantum number (n) specifies the energy level but does not directly influence the orbital angular momentum.

Key Points:

• Principal Quantum Number (n): Indicates the main energy level or shell of the electron.
• Azimuthal Quantum Number (l): Determines the shape of the orbital and the orbital angular momentum.
• Magnetic Quantum Number (m_l): Specifies the orientation of the orbital in space.
• Spin Quantum Number (m_s): Describes the intrinsic spin of the electron.

Formula for Orbital Angular Momentum:

The orbital angular momentum L is quantized and given by the formula:

L = √[l(l + 1)]ħ

Here, ħ is the reduced Planck constant. Since l directly determines the orbital angular momentum, and n influences l but not directly L, the dependency is solely on l.

Conclusion

The orbital angular momentum depends on the azimuthal quantum number (l). This relationship highlights the role of l in determining the shape and angular momentum of electron orbitals in atoms.