Classical Theory of the Atom

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1 QUANTUM CHEMISTRY

2 Classical Theory of the Atom The electron is in a shell around nucleus at a certain distance (radius, r) Electron orbits (revolves) the nucleus, like the planets around the sun. r Hydrogen What we have studied thus far.

3 Quantum Theory of the Atom We don t know exactly where the electron is. But we can say with high probability that the electron is in a region of space. This region of space is called, orbital (or electron cloud). Imagine a sphere (3D) volume around the nucleus, and somewhere in that space, we can find an electron.

4 Quantum Theory Erwin Shrödinger, Austrian Physicist, applied the idea of electrons behaving as a wave to explain electron behaviour in atoms. He developed a wave equation to describe the 3D shapes of atomic orbitals where there is a high probability that electrons are located

5 Quantum numbers The shape, size, and energy of each orbital (electron cloud) is a function of 4 quantum numbers. These quantum numbers describe the location of an electron within an atom or ion. The quantum numbers are: 1. n (principal) (angular momentum) 3. m l (magnetic) 4. m s (spin)

6 Principal Quantum number (n) Each energy level (shell) has a number called the Principal Quantum Number, n. In other words, n, indicates the main energy level occupied by the electron. n, is a positive integer: n = 1, 2, 3 7 As, n, increases, the average distance of the electron from the nucleus increases. (Energy also increases.)

7 Angular momentum quantum number ( ) Each energy level (n) has between 1 and 4 sublevels or subshells, which is represented by the angular momentum quantum number,. Values for,, is dependent on, n, and ranges from: = 0 to (n-1) For example, if n = 1, there is only one possible value for, ( =0), indicates the shape of the orbital. 4 possible shapes: s, p, d and f.

8 Angular momentum quantum number ( ) In the first shell: n =1, which means, = 0 (this is called the, s, orbital) The first shell (n), has one subshell (one value for, ) The shape of the, s-orbital is a sphere. The electron is most likely to be found in that sphere.

9 Angular momentum quantum number ( ) In the second shell: n = 2, which means, = 0, 1 (two possible values) Two values for,, thus, two possible shapes. = 0 (s orbital, spherical previous slide) = 1 (p orbital, bow-tie shape) Electron is likely to be found in that 3D volume of space Planar node, through the nucleus, which is an area of zero probability of finding an electron The Second shell (n) has two subshells (s, and p)

10 Magnetic quantum number (m l ) m l indicates orientation of an orbital around the nucleus m l depends on : m l = - to + If, =0 (s orbital sphere), then, m l = 0 (one possible value, meaning, one possible orientation) This is because, sphere has only one orientation in space.

11 Magnetic quantum number (m l ) If, = 1, then m l = -1, 0, +1 (three possible values, thus three possible orientation) Recall, when = 1, we have, p, orbital (bow-tie shape) The three orientations are designated, p x, p y, p z for the axis, and lie 90 o apart in space

12 Spin quantum number (m s ) Electrons can spin clockwise or counter-clockwise around an axis. Thus there are two values for m s m s = +1/2 (spin up); or m s = -1/2 (spin down) Spin clockwise/counter-clockwise are just arbitrary directions. It is important to understand that two electrons in the same subshell spin in opposite directions.

13 D orbitals So far we have examined the first two shells (n =1, n = 2) In the third shell: n= 3, which means, = 0, 1, 2 (three possible values, thus three possible shapes) Recall =0 (s orbital, spherical); = 1 (p orbital, bow-tie) Now, when = 2, this is called the, d-orbital (shaped like a clover leaf)

14 D orbitals When = 2, then m l = -2, -1, 0, +1, +2 (five possible values, which means, five possible orientations in space) Four of the orbitals look like clover leaf, while one looks like a peanut, with a donut around it. More complex than, p orbitals.

15 F orbitals In the fourth shell: n= 4, which means, = 0, 1, 2, 3 (4 possible shapes) When, = 3, this is called the, f, orbital.

16 F orbitals When = 3, m l = -3, -2, -1, 0, +1, +2, +3 (seven possible orientations) Even more complex (for higher, 2 nd /3 rd year University Chemistry)

17 Summary

18 Practice

19 Representing Electrons It is important to be able to describe where the electrons are with respect to energy level (shell) and subshell (s, p, d, f). Two ways: 1. Electron configuration: the concise way 2. Orbital diagrams: the visual way But first, we need to learn a few important rules!

20 Rule I The Pauli Exclusion Principle: No two electrons within an atom (or ion) can have the same four quantum numbers. In other words, only 2 electrons per orbital! Two electrons in the same energy level, and the same sublevel, they must have opposite spins! Wolfgang Pauli, Austrian Physicist.

21 Rule II Aufbau Principle: Developed by Bohr and Pauli. The principle describes the filling order of the orbitals (i.e., the order in which electrons go in) Must fill orbitals from lowest energy to highest energy. Like classical theory (Bohr), we filled the first energy shell, before filling the second and third shell. But with quantum theory, it s more complicated due to subshells. To simplify the process, a diagonal rule was devised to help you remember the order of filling the orbitals from lowest to highest energy.

22 Diagonal Rule Follow the arrows! Begin with 1s (first shell, and its sublevel) Then, fill second energy level, and s-orbital. Then, fill second shell (p orbital), then move to third shell and its s-orbital. And so on

23 Electrons allocation for each orbital Recall: s-orbital (1 orientation thus, one orbital 2 electrons max.) p-orbital (3 orientations thus, 3 orbitals 2 electrons in each)

24 Representing electrons 1) Electron Configuration (long-form)

25 Representing electrons 1) Electron Configuration (long-form) For example: Chlorine (17 electrons) Its electron configuration is 1s 2 2s 2 2p 6 3s 2 3p 5 Remember, don t go over 17 electrons, as you follow the diagonal rule (i.e., don t write, 3p 6, even though p-orbital can take 6 electrons).

26 Practice Write the electron configuration (long-form) for the following elements: H Li N F Ne

27 Representing electrons 2) Electron Configuration (Short-form) As you saw, it could be tiresome to write the long-form notation for certain atoms. There is a simplified notation (short-form) that is widely used. Steps: 1. Find the closest noble gas to the atom (or ion), without going over the number of electrons in the atom (or ion). (Hint, this noble gas should be on the end of the period above the element you are working with) 2. Write the noble gas in brackets [ ]. 3. Find where to resume by finding the next energy level. 4. Resume configuration until finished.

28 Example (short-form) notation Chlorine Long-form notation, if you recall, was: 1s 2 2s 2 2p 6 3s 2 3p 5 Neon is the noble gas at the end of the period above Chlorine. Neon has 10 electrons, thus, you can abbreviate the first 10 electrons of Chlorine with Neon. [Ne] replaces 1s 2 2s 2 2p 6 The next energy level after Neon is 3, so you start at level 3 on the diagonal rule. All levels start with, s,and finish the configuration by adding 7 more electrons to bring the total to 17. [Ne] 3s 2 3p 5

29 Practice Write the short-form electron configuration for the following atoms: S K Ca Br The End