How many electron can exist in an orbital?

An atomic orbital can hold a maximum of **two electrons**. This limitation is governed by the **Pauli exclusion principle**, which states that no two electrons in an atom can have the same set of four quantum numbers. To satisfy this principle, the two electrons in a single orbital must have opposite **spins**—one with "spin-up" and the other with "spin-down." ### Key Points: 1. **Types of Orbitals:** - **s-orbitals:** Spherical in shape. - **p-orbitals:** Dumbbell-shaped, oriented along the x, y, and z axes. - **d- and f-orbitals:** More complex shapes. 2. **Electron Capacity per Orbital:** - **Each orbital** (regardless of type) can **hold up to two electrons**. - The electrons must have **opposite spins** to occupy the same orbital. 3. **Quantum Numbers:** - **Principal Quantum Number (n):** Denotes the energy level. - **Angular Momentum Quantum Number (l):** Denotes the orbital type (s, p, d, f). - **Magnetic Quantum Number (mₗ):** Denotes the orientation of the orbital. - **Spin Quantum Number (mₛ):** Denotes the spin direction of the electron (+½ or -½). ### Example: - **Helium (He):** Has two electrons in the 1s orbital, both with opposite spins. - **Carbon (C):** Has two electrons in the 2s orbital and four electrons in the 2p orbitals (with two electrons in each of the three p orbitals, respecting the two-electron limit per orbital). ### Why Only Two Electrons? The restriction to two electrons per orbital ensures that each electron has a unique set of quantum numbers, maintaining the principles of quantum mechanics and explaining the structure of the periodic table and chemical behavior of elements. --- **Summary:** Each atomic orbital can accommodate **up to two electrons**, provided they have opposite spins.