(a) For n = 4, what are the possible values of l?

Verified step by step guidance

1. insert step 1> Identify the principal quantum number (n) given in the problem, which is n = 4.
2. insert step 2> Recall that the azimuthal quantum number (l) can take integer values from 0 to n-1.
3. insert step 3> Calculate the possible values of l by substituting n = 4 into the range 0 to n-1, which gives 0, 1, 2, and 3.
4. insert step 4> Understand that each value of l corresponds to a different type of orbital: l = 0 (s orbital), l = 1 (p orbital), l = 2 (d orbital), and l = 3 (f orbital).
5. insert step 5> Conclude that for n = 4, the possible values of l are 0, 1, 2, and 3, representing the s, p, d, and f orbitals respectively.

Key Concepts

Quantum Numbers

Quantum numbers are a set of numerical values that describe the unique quantum state of an electron in an atom. They include the principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (m_l), and spin quantum number (m_s). Each quantum number provides specific information about the electron's energy level, shape, orientation, and spin.

Principal Quantum Number (n)

The principal quantum number (n) indicates the main energy level or shell of an electron in an atom. It can take positive integer values (1, 2, 3, ...), with higher values corresponding to electrons that are further from the nucleus and have higher energy. In this case, n = 4 signifies the fourth energy level.

Azimuthal Quantum Number (l)

The azimuthal quantum number (l) defines the shape of the electron's orbital and can take on integer values from 0 to (n-1). For n = 4, the possible values of l are 0, 1, 2, and 3, which correspond to the s, p, d, and f orbitals, respectively. This concept is crucial for understanding the distribution of electrons in an atom.