chemistry laboratory report Experiment 9

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the energy of the electron increases, and the electron is farther away from the nucleus. A coliection of orbitals with the same n is called an electron shell. The value n alsolimits the values of the other two quanfum numbers.

The Angular Momentum euantum Numb er, l: 0r lr2, ..., (n _ l) The angular momentum quantum number / defines the three-aimensional shape of the orbital' The electrons of a given shell can be grouped into subshells, which are designated by letters s, P, d, orf tathu than by number. For a given shell there are n different subshells or orbitals. For example, when fr:2, I cinbe 0 and 1. Therefore there are two subshells, s subshell (/:0) andp subshell (l: l). The Magnetic Quantum Numb er, mt = J, (J* 1), ..., _1, 0, +1, ..., (t _ l), t The magnetic quantum number mr desqlbe. it. rputiul orientation of tle oiuitut in space. For an orbital whose angular quantum number is i, mr can have any integral value, including 0, between -l and 1 . Thus for a subshell of quantum number I, there are 2l + | different spatial orientations for those orbitals. For example, when l: l, mthas threevalues- -1, 0, and +l-implying that there are three typep orbitals: one with mt: _r, another with mr: 0, and a third with mr : i-L.

In summary, the first quantum number (n) locates the electron in a particular shell and determines the energy, the distance from the nucleus, and the rarrge of possible shapes. The second quantum number (/) places the electron in a particular subshell or orbital within the shell and gives the shape of the orbital. The third quantum number (m) then specifies in which orbital within the subshell the electron is located. The relationship !tlyt:" the three quantum numbers and the orbital designation are summarized in the following table.

Principal quantum Angular quantum Magnetic quantum Number Subshell n I number m

0

of orbitals 1 0

1s

2 0 0

-1, 0, +1

I

-)

2s

2p (p,, py, p,) J

I

a J

0

I

0

-1, 0, +1

-2, -1, 0, +7 , +2 5

3s

3p

3d (d*y, d),,, drr, drz-r-2, drz)

2

Spin Quantum Numbat,, tns: +y2, -y2 To describe an electron in_ an atom completely, the spin quanfum number, ms, isneeded in conjunction with the other three quantum numberi. Thi spin quantum number can have either of two values: */z or -%. A spin of +Yzis usually represented by an up alrow(t), and a spin of -%is represented by u io*, alrow (it wh"" electrons have the same m' quantum number (both+% or both -Yz),they are said to have parallel spins. When

1