Question

Question #f635a

Answer 1

Here's what I got.

Explanation:

The first part of the question wants you to find a suitable set of quantum numbers for an electron located in a 4f-orbital.

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

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Now, the number that's added to the name of an orbital tells you the energy level on which the electron resides, i.e. the principal quantum number, `n`.

In your case, an electron located in a `color(red)(4)`f-orbital will have `n=color(red)(4)`, which means that it will be located on the fourth energy level.

Now, the angular momentum quantum number, `l`, tells you the subshell in which you can find the electron. You have

• `l=0 ->` the s-subshell
• `l=1 ->` the p-subshell
• `l=2 ->` the d-subshell
• `l=3 ->` the f-subshell

Since your electron is located in the f-subshell, you will need `l = 3`.

At this point, you can have any of the seven values for the magnetic quantum number, `m_l`, that are possible for an electron located in the f-subshell

`m_l = {-3,-2, -1, color(white)(-)0, +1, +2, +3}`

Likewise, the spin quantum number, `m_s`, can take both `-1/2`, which designates an electron that has spin-down, and `+1/2`, which designates an electron that has spin-up.

Therefore, your electron can have

`{(color(white)(a)n = color(red)(4)), (color(white)(a)l= 3), (m_l = {-3, -2, -1, color(white)(-)0, +1, +2, +3}), (m_s = {-1/2, + 1/2}) :}`

For the second part of the question, you must specify the subshell in which the electron is located.

For the first electron, you have `n=2` and `l=1`. This tells you that the electron is located on the second energy level, in the p-subshell, i.e. in one of the three 2p-orbitals.

For the second electron, you have `n=4` and `l=0`. This tells you that the electron is located on the fourth energy level, in the s-subshell, i.e. in the 4s-orbital.