Question

What are the set of four quantum numbers that represent the electron gained to form the `Br` ion from `Br` atom?

Answer 1

`n = 4, l = 1, m_l = 0, m_s = -1/2`

Explanation:

As you know, there are four quantum numbers used to describe the position and spin of an electron in an atom.

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Your goal here will be to use the information provided by the electron configuration of a neutral bromine atom, `"Br"`, to determine the quantum numbers associated with the electron needed to form the bromide anion, `"Br"^(-)`.

So, bromine is located in period 4, group 17 of the periodic table and has an atomic number equal to `35`. This tells you that a neutral bromine atom has a total of `35` electrons surrounding its nucleus.

The electron configuration of a neutral bromine atom looks like this

`"Br: " 1s^2 2s^2 2p^6 3s^2 3p^6 3d^10 color(red)(4) s^2 color(red)(4)p^5`

Notice that bromine's outermost electrons, i.e. its valence electrons, are located on the fourth energy level, `n = color(red)(4)`.

The incoming electron will be added to this energy level, so right from the start you know that it must have `n=4`.

The angular momentum quantum number, `l`, tells you the subshell in which the electron is located. In this case, the incoming electron will be added to the 4p-subshell, which is characterized, much like any p-subshell, by `l=1`.

The magnetic quantum number, `m_l`, tells you the exact orbital in which the electron is located. The 4p-subshell contains a total of `3` p-orbitals

• `4p_x -> m_l = -1`
• `4p_y -> m_l = +1`
• `4p_z -> m_l = color(white)(-)0`

This is used by convention because the wave function associated with `m_l = 0` is said to be symmetric about its axis, I.e. it has no component of angular momentum about its axis, which is usually chosen as the `z` axis.

Since the neutral bromine atom already has 5 electrons in its 4p-subshell, you can say that its `4p_x` and `4p_y` orbitals are completely filled and the `4p_z` contains one electron.

The incoming electron will thus be added to the half-empty `4p_z` orbital, and so it will have `m_l = 0`.

Finally, the spin quantum number, `m_s`, tells you the spin of the electron. Because the `4p_z` already contained one electron that has spin-up, or `m_s = +1/2`, the incoming electron must have an opposite spin, and so `m_s = -1/2`.

The quantum number set that describes the incoming electron will thus be

`color(green)(|bar(ul(color(white)(a/a)color(black)(n = color(red)(4), l = 1, m_l = 0, m_s = -1/2)color(white)(a/a)|)))`

SIDE NOTE You'll sometimes see this notation used for the magnetic quantum number

• `4p_x -> m_l = -1`
• `4p_y -> m_l = color(white)(-)0`
• `4p_z -> m_l = +1`

You can use this if you want, but make sure that you are consistent.

In this notation, the wave function associated with `m_l = 0` has symmetry about the `y` axis, so make sure that you specify and keep track of this for other orbitals such as the d-orbitals of f-orbitals.