Problem 58 - Chemistry: The Central Science

Question

Give the values for \(n, l\), and \(m_{l}\) for (a) each orbital in the \(2 p\) subshell, (b) each orbital in the \(5 d\) subshell.

Step-by-Step Solution

Answer

For the 2p subshell: \(n = 2\), \(l = 1\), and \(m_l\) values are -1, 0, and +1. There are three orbitals with quantum numbers (2, 1, -1), (2, 1, 0), and (2, 1, +1). For the 5d subshell: \(n = 5\), \(l = 2\), and \(m_l\) values are -2, -1, 0, +1, and +2. There are five orbitals with quantum numbers (5, 2, -2), (5, 2, -1), (5, 2, 0), (5, 2, +1), and (5, 2, +2).

Step 1: Identify the values of n and l

In the 2p subshell, the principal quantum number n is 2 (it comes directly from the number in subshell notation), and the azimuthal quantum number l is associated with the letter p. The values of l are as follows: \(s = 0, p = 1, d = 2, f = 3, ... \) In this case, l = 1 because we are dealing with the p subshell.

Step 2: Identify the values of ml for the p subshell

For the p subshell (l = 1), the magnetic quantum number ml can take values from -l to +l, with a step of 1, including 0. So for a p subshell (l = 1), ml can be -1, 0, or +1.

Step 3: Write the values of n, l, and ml for each orbital in the 2p subshell

The 2p subshell has three orbitals, which can be represented by the quantum numbers: (a) n = 2, l = 1, ml = -1 (b) n = 2, l = 1, ml = 0 (c) n = 2, l = 1, ml = +1 For the 5d subshell:

Step 1: Identify the values of n and l

In the 5d subshell, the principal quantum number n is 5, and the azimuthal quantum number l corresponds to the letter d. As stated earlier, for the d subshell, l = 2.

Step 2: Identify the values of ml for the d subshell

For the d subshell (l = 2), the magnetic quantum number ml can take values from -l to +l, with a step of 1. So for a d subshell (l = 2), ml can be -2, -1, 0, +1, or +2.

Step 3: Write the values of n, l, and ml for each orbital in the 5d subshell

The 5d subshell has five orbitals, which can be represented by the quantum numbers: (a) n = 5, l = 2, ml = -2 (b) n = 5, l = 2, ml = -1 (c) n = 5, l = 2, ml = 0 (d) n = 5, l = 2, ml = +1 (e) n = 5, l = 2, ml = +2