Orbitals with the same principal quantum number belong to

General
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orbitals with the same principal quantum number belong to

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Orbitals with the same principal quantum number belong to

Answer:
Orbitals with the same principal quantum number belong to the same electron shell or energy level. The principal quantum number, denoted by n, determines the overall size and energy of an orbital. Here’s a detailed explanation:

Quantum Numbers and Electron Shells:

  1. Principal Quantum Number (n):

    • The principal quantum number, n, can have positive integer values (1, 2, 3, …).
    • It defines the energy level or shell of an electron within an atom.
    • Higher values of n indicate orbitals that are further from the nucleus and have higher energy.

  2. Same Principal Quantum Number:

    • Orbitals with the same n value belong to the same shell.
    • For example, all orbitals with n = 2 belong to the second electron shell.

  3. Subshells Within a Principal Shell:

    • Within each principal shell, there are subshells characterized by the azimuthal quantum number l (0 to n-1).
      • For n = 2, the possible values of l are 0 and 1, corresponding to the 2s and 2p subshells.

Example:

  • For n = 3, the third electron shell includes:
    • 3s orbital (l = 0)
    • 3p orbitals (l = 1: three orbitals with different magnetic quantum numbers m_l = -1, 0, 1)
    • 3d orbitals (l = 2: five orbitals with magnetic quantum numbers m_l = -2, -1, 0, 1, 2)

Visualization:

\begin{align*} \text{Shell (n=3)} &: \text{3s, 3p, 3d} \\ \text{Subshells} &: \text{l = 0 (s)}, \text{l = 1 (p)}, \text{l = 2 (d)} \\ \end{align*}

Conclusion:

Orbitals sharing the same principal quantum number n are part of the same electron shell or energy level. This grouping into shells determines the structure and distribution of electrons in an atom, influencing its chemical properties and bonding behavior.