Angular Momentum Quantum Number

Definition

The angular momentum quantum number, denoted as $l$, is a quantum number that describes the angular momentum of an electron within an atom. It is one of the principal quantum numbers that determine the allowed energy levels and spatial distributions of electrons in an atom.

5 Must Know Facts For Your Next Test

1. The angular momentum quantum number, $l$, can take integer values from 0 to $n-1$, where $n$ is the principal quantum number.
2. The values of $l$ correspond to the different types of atomic orbitals: $l=0$ for s orbitals, $l=1$ for p orbitals, $l=2$ for d orbitals, and $l=3$ for f orbitals.
3. The angular momentum quantum number, $l$, determines the shape and spatial distribution of the electron's wavefunction within an atom.
4. The angular momentum quantum number, $l$, is directly related to the magnitude of the orbital angular momentum of the electron, which is given by $ extbackslash sqrt{l(l+1)} extbackslash hbar$.
5. The angular momentum quantum number, $l$, along with the principal quantum number, $n$, and the magnetic quantum number, $m_l$, completely specify the state of an electron in an atom.

Review Questions

• Explain the relationship between the angular momentum quantum number, $l$, and the types of atomic orbitals.
  • The angular momentum quantum number, $l$, determines the type of atomic orbital an electron can occupy. Specifically, $l=0$ corresponds to s orbitals, $l=1$ corresponds to p orbitals, $l=2$ corresponds to d orbitals, and $l=3$ corresponds to f orbitals. The value of $l$ is directly related to the shape and spatial distribution of the electron's wavefunction within the atom, with higher values of $l$ resulting in more complex orbital shapes.
• Describe how the angular momentum quantum number, $l$, is related to the magnitude of the orbital angular momentum of an electron.
  • The angular momentum quantum number, $l$, is directly related to the magnitude of the orbital angular momentum of an electron. The orbital angular momentum is given by the expression $ extbackslash sqrt{l(l+1)} extbackslash hbar$, where $ extbackslash hbar$ is the reduced Planck constant. This means that as the value of $l$ increases, the magnitude of the orbital angular momentum also increases, reflecting the more complex motion of the electron within the atom.
• Explain how the angular momentum quantum number, $l$, along with the other quantum numbers, completely specify the state of an electron in an atom.
  • The angular momentum quantum number, $l$, along with the principal quantum number, $n$, and the magnetic quantum number, $m_l$, together completely specify the state of an electron in an atom. The principal quantum number, $n$, determines the energy level of the electron, while the angular momentum quantum number, $l$, determines the type of orbital the electron occupies. The magnetic quantum number, $m_l$, then describes the orientation of the angular momentum of the electron within the atom. By knowing these three quantum numbers, one can fully characterize the state of an electron and its behavior within the atomic structure.

Related terms

Orbital Angular Momentum: The angular momentum associated with the motion of an electron around the nucleus of an atom, which is quantized and described by the angular momentum quantum number.

Magnetic Quantum Number: The magnetic quantum number, denoted as $m_l$, is a quantum number that describes the orientation of the angular momentum of an electron in an atom with respect to an external magnetic field.

Electron Configuration: The arrangement of electrons in an atom, which is determined by the principal quantum number, $n$, and the angular momentum quantum number, $l$.