Question #254fb

1 Answer
Apr 25, 2017

Answer:

Here's what I got.

Explanation:

As you know, we can use four quantum numbers to describe the position and the spin of an electron in an atom.

figures.boundless.com

For the first set, you have

#n =3 and m_l = -2#

The principal quantum number, #n#, tells you the energy level, or energy shell, on which the electron resides.

The energy shell determines the energy subshell, which is given by the angular momentum quantum number, #l#.

In this case, you have

#l = {0, 1, 2}#

The magnetic quantum number, #m_l#, tells you the orbital in which the electron is located. As you can see on the table, #m_l# depends on #l#.

More specifically, #m_l = -2# is one of the five orbitals available for

#l = 2#

which describes the #d# subshell.

Now, every orbital can hold a maximum of #2# electrons of opposite spins, as given by the Pauli Exclusion Principle. This means that a maximum of #2# electrons can share

#n = 3 and m_l = -2 -> color(darkgreen)(ul(color(black)("max 2 e"^(-))))#

For the second set, you have

#n = 5 and l= 0 #

This time, you have the fifth energy level and the #s# subshell. As you can see, the magnetic quantum number can only take one value for #l=0#

#m_l = 0 -># the #s# orbital

Once again, you are dealing with a single orbital, which means that you will have a maximum of #2# electrons that can share

#n = 5 and l = 0 -> color(darkgreen)(ul(color(black)("max 2 e"^(-))))#

Finally, you have

#n=4, l=3, and m_l = -1#

This time, you are working on the fourth energy level, in the #f# subshell, which is described by #l=3#.

Once again, the fact that you have a single value for #m_l# tells you that you are working with a single orbital, which means that you will have a maximum of #2# electrons that can share

#n=5, l=3, and m_l = -1 -> color(darkgreen)(ul(color(black)("max 2 e"^(-))))#