Question

Identify the element whose last electron would have the following four quantum numbers:

3, 1, -1, +1/2
4, 2, +1, +1/2
6, 1, 0, -1/2
4, 3, +3, -1/2
2, 1, +1, -1/2

Answer 1

The element whose last electron would have the given set of four quantum numbers is in the 3p subshell.

Step-by-step explanation:

In order to identify the element whose last electron has the given set of four quantum numbers, we need to understand what each quantum number represents. The four quantum numbers are: n, l, m_l, m_s. The first number n represents the principal quantum number, which determines the energy level of the electron. The second number l represents the azimuthal quantum number, which determines the shape of the orbital. The third number m_l represents the magnetic quantum number, which determines the orientation of the orbital within a given subshell. The last number m_s represents the spin quantum number, which determines the spin of the electron.

In the given set of quantum numbers, the values are as follows:

• 3, 1, -1, +1/2
• 4, 2, +1, +1/2
• 6, 1, 0, -1/2
• 4, 3, +3, -1/2
• 2, 1, +1, -1/2

Now, we need to match these quantum numbers with the allowed values for the various subshells. Based on the rules for the quantum numbers:

1. For n = 3 and l = 1, the only allowed value for m_l is -1. The allowed value for m_s is +1/2. Thus, the electron is in the 3p subshell.
2. For n = 4 and l = 2, the only allowed value for m_l is +1. The allowed value for m_s is +1/2. Thus, the electron is in the 4d subshell.
3. For n = 6 and l = 1, the only allowed value for m_l is 0. The allowed value for m_s is -1/2. Thus, the electron is in the 6p subshell.
4. For n = 4 and l = 3, the only allowed value for m_l is +3. The allowed value for m_s is -1/2. However, the maximum value of l is 2, so this set of quantum numbers is not allowed.
5. For n = 2 and l = 1, the only allowed value for m_l is +1. The allowed value for m_s is -1/2. Thus, the electron is in the 2p subshell.

Based on these calculations, we can determine that the element with the given set of quantum numbers is in the 3p subshell.

Answer 2

The identification of elements is based on the principle quantum number (energy level), azimuthal quantum number (subshell), magnetic quantum number (orbital orientation), and the spin quantum number. The Pauli exclusion principle mandates unique sets of these numbers for each electron in an atom. Some of the provided quantum numbers indicate a specific subshell occupation, while at least one set is not valid.

Step-by-step explanation:

To identify the element whose last electron has certain quantum numbers, we must understand the meaning of each quantum number:

• The principal quantum number (n) indicates the energy level or shell.
• The azimuthal quantum number (l) defines the subshell or shape of the orbital (0 equals s, 1 equals p, 2 equals d, and 3 equals f).
• The magnetic quantum number (m₁) declares the orientation of the orbital within the subshell.
• The spin quantum number (m₂) indicates the electron's spin direction, where +1/2 refers to 'spin up' and -1/2 to 'spin down'.

Using these rules, we can identify the elements based on the given quantum numbers:

1. {3, 1, -1, +1/2} corresponds to an element with its last electron in the 3p subshell, with a 'spin up' orientation.
2. {4, 2, +1, +1/2} is an electron in the 4d subshell with a 'spin up' orientation.
3. {6, 1, 0, -1/2} is in the 6p subshell with a 'spin down' orientation.
4. {4, 3, +3, -1/2} cannot exist because the magnetic quantum can only go from -l to +l, and the maximum m₁ for l=3 is +3.
5. {2, 1, +1, -1/2} is an electron in the 2p subshell with a 'spin down' orientation.

The Pauli exclusion principle tells us that no two electrons in the same atom can have the same set of quantum numbers. Hence, the sets of quantum numbers for each electron must be unique, and the second electron in a helium atom fills the 1s orbital with opposite spin to obey this rule.

The question seems to be asking for identification of elements based on their electron configurations, but only some of the provided sets of quantum numbers are valid due to quantum mechanical rules.