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Chapter 7: Problem 89

Give a possible set of values of the four quantum numbers for all the electrons in a boron atom and a nitrogen atom if each is in the ground state.

Short Answer

Expert verified
For a boron atom (B, atomic number 5) in the ground state, the possible sets of quantum numbers are: 1. (n = 1, l = 0, m_l = 0, m_s = +1/2) 2. (n = 1, l = 0, m_l = 0, m_s = -1/2) 3. (n = 2, l = 0, m_l = 0, m_s = +1/2) 4. (n = 2, l = 0, m_l = 0, m_s = -1/2) 5. (n = 2, l = 1, m_l = -1, m_s = +1/2) For a nitrogen atom (N, atomic number 7) in the ground state, the possible sets of quantum numbers are: 1. (n = 1, l = 0, m_l = 0, m_s = +1/2) 2. (n = 1, l = 0, m_l = 0, m_s = -1/2) 3. (n = 2, l = 0, m_l = 0, m_s = +1/2) 4. (n = 2, l = 0, m_l = 0, m_s = -1/2) 5. (n = 2, l = 1, m_l = -1, m_s = +1/2) 6. (n = 2, l = 1, m_l = 0, m_s = +1/2) 7. (n = 2, l = 1, m_l = 1, m_s = +1/2)

Step by step solution

01

First, we need to know the atomic number of each atom, which corresponds to the number of protons and electrons in its neutral state. Looking at a periodic table, we find out that boron has an atomic number of 5 and nitrogen has an atomic number of 7. The electron configuration shows how the electrons are arranged in the atomic orbitals. Following the Aufbau principle, Pauli Exclusion Principle, and Hund's rule, the electron configurations for the ground state of both atoms can be written as follows: Boron (B, atomic number 5): 1s²2s²2p¹ Nitrogen (N, atomic number 7): 1s²2s²2p³ #Step 2: Identify the quantum numbers for each electron in the electron configuration.#

There are four quantum numbers: principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (m_l), and the spin quantum number (m_s). The principal quantum number (n) represents the energy level of the electron. For example, n = 1 for the 1s orbital, n = 2 for 2s and 2p orbitals, and so on. The azimuthal quantum number (l) represents the shape of the orbital. For s orbitals, l = 0; for p orbitals, l = 1, and so on. The magnetic quantum number (m_l) represents the orientation of the orbital in space. The range of m_l values is from -l to +l, for a total of (2l + 1) orbitals. The spin quantum number (m_s) represents the electron's spin (clockwise or counterclockwise) and can either be +1/2 or -1/2. Now let's find the quantum numbers for all the electrons in the electron configurations of both atoms. #Step 3: Calculate the sets of quantum numbers for electrons in a boron atom.#
02

Boron (B, atomic number 5): 1s²2s²2p¹ 1st electron (1s orbital): n = 1 l = 0 m_l = 0 m_s = +1/2 2nd electron (1s orbital): n = 1 l = 0 m_l = 0 m_s = -1/2 3rd electron (2s orbital): n = 2 l = 0 m_l = 0 m_s = +1/2 4th electron (2s orbital): n = 2 l = 0 m_l = 0 m_s = -1/2 5th electron (2p orbital): n = 2 l = 1 m_l = -1 (we fill the lowest m_l value first) m_s = +1/2 #Step 4: Calculate the sets of quantum numbers for electrons in a nitrogen atom.#

Nitrogen (N, atomic number 7): 1s²2s²2p³ 1st electron (1s orbital): n = 1 l = 0 m_l = 0 m_s = +1/2 2nd electron (1s orbital): n = 1 l = 0 m_l = 0 m_s = -1/2 3rd electron (2s orbital): n = 2 l = 0 m_l = 0 m_s = +1/2 4th electron (2s orbital): n = 2 l = 0 m_l = 0 m_s = -1/2 5th electron (2p orbital): n = 2 l = 1 m_l = -1 m_s = +1/2 6th electron (2p orbital): n = 2 l = 1 m_l = 0 m_s = +1/2 7th electron (2p orbital): n = 2 l = 1 m_l = 1 m_s = +1/2 These are the sets of quantum numbers for all electrons in the ground state for a boron atom and a nitrogen atom.

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