Formula: Isotope Representation

PICTURES OF ATOMIC ORBITALS

L=0

The 1s orbital
The 2s orbital
The 3s orbital
The 4s orbital

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L=1

The 2p_x orbital
The 2p_y orbital
The 2p_z orbital

The 3p_x orbital
The 3p_y orbital
The 3p_z orbital

The 4p_x orbital
The 4p_y orbital
The 4p_z orbital

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L=2

The 3d_z² orbital
The 3d_yz orbital
The 3d_xz orbital
The 3d_xy orbital
The 3d_x2_-y2 orbital

The 4d_z² orbital
The 4d_yz orbital
The 4d_xy orbital
The 4d_xz orbital
The 4d_x2_-y2 orbital

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L=3

The 4f_z3 orbital
The 4f_xz2 orbital
The 4f_yz2 orbital
The 4f_xyz orbital
The 4f_z(x2_-y2₎ orbital
The 4f_x(x2_-3y2₎ orbital
The 4f_y(3x2_-y2₎ orbital

ELECTRONIC CONFIGURATION

Determining Electron Configuration

One of the skills you will need to learn to succeed in freshman chemistry is being able to determine the electron configuration of an atom. An electron configuration is basically an account of how many electrons there are, and in what orbitals they reside under "normal" conditions. For example, the element hydrogen (H) has one electron. We know this because its atomic number is one (1), and the atomic number tells you the number of electrons. Where does this electron go? The one electron of hydrogen goes into the lowest energy state it possibly can, which means it will start at "level" one and goes into "s" orbitals first. We say that hydrogen has a "[1s¹]" electron configuration. Looking at the next element on the Periodic Table --helium, or He -- we see it has an atomic number of two, so two electrons. Since " s" orbitals can hold up to two electrons, helium has an electron configuration of "[1s²]".

What about larger atoms? Let's look at carbon, with an atomic number of 6. Where do its 6 electrons go?

• First two: 1s²
• Next two: 2s²
• Last two: 2p²

We can therefore say that carbon has the electron configuration of "[1s²2s²2p²]".

The table below shows the subshells, the number of orbitals, and the maximum number of electrons allowed:

Subshell	Number of Orbitals	Maximum Number of Electrons
s	1	2
p	3	6
d	5	10
f	7	14

The Abridged (shortened) Periodic Table below shows the electron configurations of the elements. Notice for space reasons we sometimes leave off a portion of the electron configuration. For example, look at argon (Ar), element 18. The table below shows its electron configuration as "[3s²3p⁶]" (remembering that "p" orbitals can hold up to six (6) electrons). Its actual electron configuration is:

Ar = [1s²2s²2p⁶3s²3p⁶]

Sometimes you will see the notation: "[Ne]3s²3p⁶", which means to include everything that is in neon (Ne, 10) plus the stuff in the "3"-level orbitals.

ATOMIC STRUCTURE

Atomic Models and the Quantum Numbers

There are different models of the structure of the atom. One of the first models was created by Niels Bohr, a Danish physicist. He proposed a model in which electrons circle the nucleus in "orbits" around the nucleus, much in the same way as planets orbit the sun. Each orbit represents an energy level which can be determined using equations generated by Planck and others discussed in more detail below. The Bohr model was later proven to be incorrect, but provides a useful model for building an explanation.

The "accepted" model is the quantum model. In the quantum model, we state that the electron cannot be found precisely, but we can predict the probability, or likelihood, of an electron being at some location in the atom. You should be familiar with quantum numbers, a series of three numbers used to describe the location of some object (like an electron) in three-dimensional space:

1. n: the principal quantum number, an integer value (1, 2, 3...) that is used to describe the quantum level, or shell, in which an electron resides. The principal quantum number is the primary number used to determine the amount of energy in an atom. Using one of the first important equations in atomic structure (developed by Niels Bohr), we can calculate the amount of energy in an atom with an electron at some value of n:

   En = -

   Rhc n2

   where:
   R = Rydberg constant, a value of 1.097 X 10⁷ m^-1
   c = speed of light, 3.00 X 10⁸ m/s
   h = Planck's constant, 6.63 X 10 ^-34 J-s
   n = principal quantum number, no unit

   For example, how much energy does one electron with a principal quantum number of n= 2 have?

   En = - Rhc n2

   or

   En = - (1.097x107 m-1 ∗ (6.63x10-34 J•s)∗(3.0x108 m•s-1) 22

   = 5.5x10-19 J

   You might ask, well, who cares? In addition to the importance of knowing how much energy is in an atom (a very important characteristic!), we can also derive, or calculate, other information from this energy value. For example, can we see this energy? The table below suggests that we can. For example, suppose that an electron starts at the n=3 level (we'll call this the excited state) and it falls down to n=1 (the ground state). We can calculate the change in energy using the equation:

   ΔE = hv = RH

   1 ni2

   -

   1 nf2

   Where:
   ΔE = change in energy (Joules)
   h = Planck's constant with a value of 6.63 x 10^-34 (J-s)
   ν is frequency (s^-1)
   R_H is the Rydberg constant with a value of 2.18 x 10^-18J.
   n_i is the initial quantum number
   n_f is the final quantum number

   Using the equation below, we can calculate the wavelength and the frequency of the energy. The wavelength and the frequency give us information about how we might "see" the energy:

   vλ = c

   Where:
   ν = the frequency of radiation (s^-1)
   λ = the wavelength (m)
   c = the speed of light with a value of 3.00 x 10⁸ m/s in a vacuum
   

   Speed of light =	3.00E+08
   Rydberg constant =	2.18E-18
   Planck's constant =	6.63E-34
   Excited state, n =	3	4	5
   Ground state, n =	2	2	2
   Excited state energy (J)	2.42222E-19	1.363E-19	8.72E-20
   Ground state energy (J)	5.45E-19	5.45E-19	5.45E-19
   ΔE =	-3.02778E-19	-4.09E-19	-4.58E-19
   ν =	4.56678E+14	6.165E+14	6.905E+14
   λ(nm) =	656.92	486.61	434.47

2. l ("el", not the number 1): the azimuthal quantum number, a number that specifies a sublevel, or subshell, in an orbital. The value of the azimuthal quantum number is always one less than the principal quantum number n. For example, if n=1, then "el"=0. If n=3, then l can have three values: 0,1, and 2. The values of l are typically not identified as "0, 1, 2, and 3" but are more commonly called by their historic names, "s, p, d, and f", respectively. Since the quantum numbers were discovered through the study of light and lines on an electromagnetic spectra, chemists identified the lines by their quality:sharp, principal, diffuse and fundamental. The table below shows the relationship:

   Value of l	Subshell designation
   0	s
   1	p
   2	d
   3	f

3. m: the magnetic quantum number. Each subshell is composed of one or more orbitals. In the study of light, it was discovered that additional lines appeared in the spectra produced when light was emitted in a magnetic field. The magnetic quantum number has values between -l and +l. When l =1, for example, m can have three values: -1, 0, and +1. Because you know from the chart above that the subshell designation for l =1 is "p", you now know that the p orbital has three components. In your study of chemistry, you will be presented with p_x, p_y, and p_z. Notice how the subscripts are related to a three-dimensional coordinate system, x, y, and z. The chart below shows a summary of the quantum numbers:

   Principal Quantum Number (n)	Azimuthal Quantum Number (l)	Subshell Designation	Magnetic Quantum Number (m)	Number of orbitals in subshell
   1	0	1s	0	1
   2	0 1	2s 2p	0 -1 0 +1	1 3
   3	0 1 2	3s 3p 3d	0 -1 0 +1 -2 -1 0 +1 +2	1 3 5
   4	0 1 2 3	4s 4p 4d 4f	0 -1 0 +1 -2 -1 0 +1 +2 -3 -2 -1 0 +1 +2 +3	1 3 5 7

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Chemists care about where electrons are in an atom or a molecule. In the early models, we believed that electrons move like billiard balls, and followed the rules of classical physics. The graphic below attempts to show that earlier models thought that we could identify the exact path, position, velocity, etc. of an electron or electrons in an atom:

A more accurate picture is that the electron(s) reside in a "cloud" that surrounds the nucleus of the atom. This concept is shown in the graphic below:

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