Which of the following represent impossible combinations of n and l? (a) 1p (b) 4s (c) 5f (d) 2d

Verified step by step guidance

1. Understand the quantum numbers: The principal quantum number, n, can be any positive integer (1, 2, 3, ...). The azimuthal quantum number, l, can be any integer from 0 to n-1.
2. Identify the possible values of l for each n: For n=1, l can only be 0 (s orbital). For n=2, l can be 0 (s) or 1 (p). For n=3, l can be 0 (s), 1 (p), or 2 (d). For n=4, l can be 0 (s), 1 (p), 2 (d), or 3 (f).
3. Analyze each option: (a) 1p: Here, n=1 and l=1. Since l must be less than n, this is impossible.
4. Analyze each option: (b) 4s: Here, n=4 and l=0. This is possible because l=0 is within the range for n=4.
5. Analyze each option: (c) 5f: Here, n=5 and l=3. This is possible because l=3 is within the range for n=5.

Key Concepts

Quantum Numbers

Quantum numbers are a set of four numbers that describe the unique quantum state of an electron in an atom. The principal quantum number (n) indicates the energy level, while the azimuthal quantum number (l) defines the shape of the orbital. Each value of n allows for specific values of l, which must be less than n.

Allowed Values of l

The azimuthal quantum number (l) can take on integer values from 0 to n-1 for a given principal quantum number (n). For example, if n=2, l can be 0 (s orbital) or 1 (p orbital), but not 2. This restriction is crucial for determining valid combinations of n and l.

Orbital Designations

Orbitals are designated by a combination of the principal quantum number (n) and the azimuthal quantum number (l), represented by letters (s, p, d, f). For instance, 'p' corresponds to l=1, 'd' to l=2, and 'f' to l=3. Understanding these designations helps identify which combinations of n and l are valid or impossible.