# chemical properties of matter by marcusbuggs

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```									PHY1003 Properties of Matter

Atomic and molecular structure
I. Quantum number notation
The wave functions for the hydrogen atom are determined by the values of three quantum numbers n, l and ml.

n l

principal quantum number (determines the energy) orbital quantum number (determines the magnitude of the orbital angular momentum) of orbital angular momentum in a specified axis direction)

ml magnetic quantum number (determines the component
A fourth quantum number, ms (the spin quantum number) is necessary to label completely the state of the electron in a hydrogen atom (determines the z-component of the spin angular momentum).

Quantum number notation
For many-electron atoms, in the central-field approximation, we can still label a state using the four quantum numbers (n, l, ml and ms). In general, the energy of the state now depends on both

n and l.

Restrictions on the values of the quantum numbers (the same as for the hydrogen atom)

n≥1

n = 1, 2, 3...
l = 0, 1, 2 . . . (n − 1)

m l = −l . . . + l
1 ms = ± 2

The exclusion principle
The exclusion principle states that no two electrons can occupy the same quantum-mechanical state in a given system. This means that no two electrons in an atom can have the same values of all four quantum numbers n, l, ml and ms.

Wolfgang Ernst Pauli (1900-1958)

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PHY1003 Properties of Matter

Quantum number notation
The radial extent of the wave functions increases with the principal quantum number n, and we can speak of a region of space associated with a particular value of n as a shell.

n = 1 K shell n = 2 L shell

n = 3 M shell n = 4 N shell

States with the same n but different l form subshells. These subshells are often lebelled with letters.

l = 0 s state l = 1 p state l = 2 d state

l = 3 f state l = 4 g state

Remember that

l = 0, 1, 2 . . . (n − 1)

Quantum states of electrons n
1 2 2 3 3 3 4 4 4 4

l
0 0 1 0 1 2 0 1 2 3

ml
0 0 -1,0,1 0 -1,0,1 -2,-1,0,1,2 0 -1,0,1 -2,-1,0,1,2 -3,-2,-1,0,1,2,3

spectroscopic No notation states 1s 2 2s 2p 3s 3p 3d 4s 4p 4d 4f 2 6 2 6 10 2 6 10 14

Shell K L

8

18

M

32

N

The maximum number of electrons in a shell is

2n2

Graund-state electronic configurations
Element
Hydrogen Helium Lithium Beryllium Boron Carbon … Neon … Aluminium Silicon … Titanium

Symbol Atomic No H He Li Be B C Ne Al Si Ti
1 2 3 4 5 6 10 13 14 22

Electronic configuration
1s 1s2 1s22s 1s22s2 1s22s22p 1s22s22p2 1s22s22p6 1s22s22p63s23p 1s22s22p63s23p2 1s22s22p63s23p64s23d2

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PHY1003 Properties of Matter

Graund-state electronic configurations
On the basis of the electronic configuration we can understand the regularities in the chemical behaviour of the elements, displayed in the periodic table. Chemical activities are mainly determined by the electrons in the outermost shell (or the two outermost shells). It is convenient to describe an atom as composed of ion core and valence electrons.

atom = ion core + valence electrons
nucleus + tightly bound electrons outer shell electrons

Graund-state electronic configurations
Core and valence electrons

C

[1s2]2s22p2

Ne [1s22s22p6]

Si [1s22s22p6] 3s23p2
[core electrons] valence electrons
He [1s2] Li [1s2]2s Na [1s22s22p6]3s F [1s2]2s22p5 Ne [1s22s22p6]

Cl [1s22s22p6]3s23p5 Ar [1s22s22p63s23p6]

The periodic law
Without entering into details, I will give the conclusions I then arrived at, in the very words I used:-"1. The elements, if arranged according to their atomic weights, exhibit an evident periodicity of properties.
The Periodic Law of the Chemical Elements. Journal of the Chemical Society, 55, 634-56 (1889) By Professor MENDELÉEFF

Dmitrii Mendeleev (1834-1907)

The elements, if arranged according to the number of the positive charges of their nuclei, exhibit periodicity of properties.

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PHY1003 Properties of Matter

The periodic table

Types of molecular bonds
I. Ionic bond − transfer of electrons of one atom to another. II. Covalent bond − sharing of electrons; directional bond.

H

H
1 and 5 eV.

H2

Bond energies between

Types of molecular bonds
III. van der Waals bonds − interaction between electric dipole moments of atoms and molecules. Typical energy < 0.1 eV. Weak bonding.

IV. Hydrogen bond − caused by polarisation due to H+. Bond energy < 0.5 eV.
van der Waals and hydrogen bonds are weaker than ionic and covalent bonds.

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PHY1003 Properties of Matter

Structure of molecules

Exist in all three states: gas, liquid and solid.

Shapes of molecules & symmetry
Linear molecules Planar molecules 3D molecules 109.48° 109.48°

120° 120°

CH4

180° bond angle 180°

Molecular spectra
I. Rotational energy levels

E =

1 2 Iω 2

L = Iω
m1

r0 m2 r1 r2

-2 L2 l (l + 1) h E= = 2I 2I
l = 0, 1, 2 . . .

E

l = 4 E =10 h2 /I l = 3 E =6 h 2/I l = 2 E =3 h 2/I l = 1 E =h2/I l=0 E=0

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PHY1003 Properties of Matter

Molecular spectra
E= L2 l (l + 1) h2 = 2I 2I
mr = m1 m 2 reduced mass m 1 + m2
r0 m1 r1 r2 m2

m1 r 1 = m 2 r 2
r1 = m2 r0 m1 + m2

r0 = r1 + r2

r2 =

m1 r0 m1 + m2

2 2 I = m 1 r1 + m2 r2 =

m 1 m2 2 r = mr r 2 0 m1 + m2 0
l (l + 1) h2 l (l + 1) h 2 = 2 2I 2m r r0

I = mr r 2 0

E=

Molecular spectra
II. Vibrational energy levels

m1
En = n+ 1 1 - Λ hω = n + h 2 2 mr

Λ

m2

n = 0, 1, 2 . . .

En

m1 m 2 mr = m 1 + m2

7n = 3 E n = hω 2 5n = 2 E n = hω 2 3n = 1 E n = hω 2 1n = 0 E n = hω 2

Molecular spectra
(n)

Vibrational levels IR spectroscopy

Rotational levels

(l)

Microwave spectroscopy (microwave and far IR)

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