Imagine a universe in which the four quantum numbers can have the same possible values as in our universe except that the angular-momentum quantum number l can have integral values of 0, 1, 2...n + 1 (instead of 0, 1, 2..., n - 1). (c) Draw an orbital-filling diagram for the element with atomic number 12.

Verified step by step guidance

1. Step 1: Understand the quantum numbers. In this universe, the principal quantum number (n) can have values of 1, 2, 3, etc. The angular momentum quantum number (l) can have values from 0 to n+1. The magnetic quantum number (ml) can have values from -l to +l. The spin quantum number (ms) can have values of -1/2 or +1/2.
2. Step 2: The atomic number of an element is equal to the number of protons in its nucleus, which is also equal to the number of electrons in a neutral atom. So, an element with atomic number 12 has 12 electrons.
3. Step 3: Start filling the orbitals according to the Aufbau principle, which states that electrons fill the lowest energy orbitals first. In this universe, the order of filling would be 1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 4f, 5s, etc.
4. Step 4: Fill the orbitals with the 12 electrons. The 1s orbital can hold 2 electrons, the 2s orbital can hold 2 electrons, the 2p orbital can hold 6 electrons, and the 3s orbital can hold 2 electrons. So, the electron configuration would be 1s2 2s2 2p6 3s2.
5. Step 5: Draw the orbital filling diagram. Each box or line in the diagram represents an orbital, and each arrow represents an electron. The direction of the arrow represents the spin of the electron. Fill the orbitals in the order mentioned in step 3, and follow Hund's rule, which states that each orbital in a subshell is singly occupied before any orbital is doubly occupied.

Key Concepts

Quantum Numbers

Quantum numbers are sets of numerical values that describe the unique quantum state of an electron in an atom. There are four quantum numbers: the principal quantum number (n), which indicates the energy level; the angular momentum quantum number (l), which describes the shape of the orbital; the magnetic quantum number (m_l), which specifies the orientation of the orbital; and the spin quantum number (m_s), which indicates the direction of the electron's spin.

Orbital Filling Order

The order in which electrons fill atomic orbitals is determined by the Aufbau principle, which states that electrons occupy the lowest energy orbitals first. The typical filling order follows the sequence dictated by the n + l rule, where orbitals are filled based on the sum of their principal and angular momentum quantum numbers. This order is crucial for constructing the electron configuration of an element.

Electron Configuration of Element 12

Element 12 is magnesium (Mg), which has an atomic number of 12, indicating it has 12 electrons. The electron configuration is determined by filling the orbitals according to the modified quantum number rules. In this case, with the angular momentum quantum number l allowed to take values up to n + 1, the electron configuration for magnesium would be 1s² 2s² 2p⁶ 3s², reflecting the distribution of its electrons across the available orbitals.