Electrons in An Atom

Small particles such as atoms, molecules, nuclei and particularly electrons, obey different laws regarding energy and motion, than larger objects such as billiard balls. Large molecules obey laws of motion of Isaac Newton ( laws of classical physics ) but small particles obey a kind of mechanics called quantum mechanics. It is the fundamental theory used to explain the behavior of electrons and other small particles.

Postulates of the Quantum Theory

1. Atoms and molecules can only exist in certain states, characterized by definite amounts of

energy. When atom or molecule changes its state, it must absorb or emit an amount of energy just sufficient to bring it to another state.

Motion of electrons about the nucleus and the charge interactions among electrons and between the electrons and the nucleus give rise to some form of energy. This kind of energy

is called electronic energy. Only certain values of electronic energy are allowed to an atom.

  • Emphasize the emission or absorption of enough energy by an atom in going from one allowed electronic state to another.

The energy of systems that can exist only in discrete states is said to be quantized.

2. When atoms or molecules absorb or emit light in the process of changing their energies, the wavelength of the light is related to the magnitude of the energy change E by the equation:

E= hc = h,  = c

 

Where h is a physical constant called Planck’s constant, and c is the speed of light.

h = 6.626 x 10-34 joule. sec

c = 2.998 x 108 meters/sec.

3. The allowed energy states of atoms and molecules can be described by sets of numbers called quantum numbers.

Each electronic state of an atom is described by a group of quantum numbers associated with the individual electron in the atom.

Atomic Spectra

Atoms exposed to high energy become excited and give off energy in the form of radiation. The type of radiation emitted depends on the excitation which is used. Heated metal gives off visible light which contains all component colors.

continuous spectrum contains light at all wavelengths

Sodium Chloride few bright lines which indicate few wavelengths at which sodium atoms are emitted. This is atomic spectrum of sodium. Since it contains light at only specific wavelengths, it is said to be discrete.

Every atom has its own characteristic spectrum.

4

3

nhi nl0 =

emission of 2

energy

nlonhi =absorption

of energy 1

E = hc = E photon

Photon: a ray of light consists of photons. Photons are particulate in nature. Each photon has an energy which is inversely proportional to its wavelength.

EXAMPLE:

Excited sodium atoms may emit radiation having a wavelength of 4890  (anstron ) .

a. What is the energy in joules of the photons in this radiation?

b. What is the energy of a mole of these photons in kJ? in kcal?

Solution:

a. E = E photon = hc

h = 6.626 x 10 joule sec

c = 2.998 x 10 meters/sec

 = 5890 ; this has to be changed to meters

1 A = 1 x 10-10 meters

 = 5890 x 1 x 10 -10 m = 5.890 x 10-7 m

1

Ephoton = 6.626 x 10-34 joule. sec x 2.998 x 108 m/ sec. = 3.37 x 10-19 joules

5.890 x 10-7 m

b. 1 mole = 6.02 x 1023

= 3.37 x 10-19 joules x 6.02 x 1023 photons

1 photon 1 mole

= 2.03 x 10 5 joules/moles

= 203 kjoules/mole

Since 1 kcal = 4.184 kj;

Ephotons = 203 kJ/mole x 1 kcal/4.184 kJ

= 48.5 kcal/mole

Note:

1 joule/particle = 6.02 x 1020 kJ/mole = 1.44 x 1020 kcal / mole

The Bohr Model of the Atom

Bohr assumed hydrogen atom to consist of a central proton around which an electron moved in a circular orbit as the earth moves around the sun. Related the force of attraction of the proton for the electron to centrifugal force in circular motion of the electron.

Angular momentum, mvr, of the electron; where mvr = nh / 2 where m = mass of electron, v = speed, r = radius of the orbit, n = a quantum number = any positive integral value 1, 2, 3, 4...

This quantum condition restricted the allowed energies of the hydrogen atom to those values given by

E = -B/n2

n = quantum #

B = 2.179 x 10-18 joules

OR

E = -Kz2 / n2

K = 2.179 x 10-18 joules

z = at # z = 1 for hydrogen

Bohr assumed zero energy to be at the point where the proton and electron were completely separated; that is the state where the atom was ionized. As the electron approaches the nucleus, the atom becomes more stable, so its energy lies below zero and is negative in all of its allowed states. Lowest energy state is when n = 1 and the energy = B. This level is called the ground state of the atom. This is the state in which the atom is ordinarily found. When n  higher #, the energy becomes higher (less negative) than the energy of the ground state. The atom is said to be excited.

EXAMPLE

Find the wavelength in  of the line in the Balmer series that is associated with

n = 4 n = 2 transition.

Answer

E = -B / n2

E4 = -B / 16

E2 = -B / 4

In joules: E4 = -( 2.179 x 10-18 J ) / 16 = -1.6362 x 10-19J

E2 = -( 2.179 x 10-18J ) / 14 = -5.448 x 10-19J

The energy of the photon equals the change in energy  = E2 - E4

Ephoton= ( -1.362 + 5.448 ) x 10-19 J = 4.086 x 10-19 J

Ephoton = hc / 

 = hc/ Ephoton

 = 6.626 x 10-34 joule. sec x 2.998 x 10-7 m

4.086 x 10-19 J

4.186 x 10-7m x 1A = 4861 A

1x10-10m

Note: Bohr radius = 0.529 A when n =1

r = 0.529 n2 A

v = 2.18 x 107 meters / sec

n

Note:  = En1 - En2 = 2.179 x 10-18 ( 1/n12 -1/n22)J; n1 < n2

Heisenberg Uncertainty Principle: It is impossible to determine accurately both the momentum and the position of an electron simultaneously, hence we speak of the probability of finding an electron at a given location within the atom.

Electron Arrangements in Atoms

Each electron in an atom is described (named) by a set of 4 numbers: n, l, ml , ms

1. n. represents the energy of an electron. n = 1, 2, 3, 4, 5 ... but not 0. Electrons with the

same n move about roughly the same level or shell. n = periods on the periodic table.

2. Each level of electrons is made up of one or more sublevels or sub-shells. These are

denoted by l. This determines the geometric shape of the electron cloud. l

is limited to take on the values l = 0, 1, 2, ... (n1)

In general, in nthlevels, there aren sublevels.

l (sublevel) = 0 1 2 3 4 5

Notation s p d f g h

3. Each sublevel contains one or more orbitals designated by m1. This number is

associated with the orientation of the electron cloud with respect to a given direction.

In general, within a given sublevel l, there will be (2l+1) orbitals;each with the same

energy. Electrons fit into orbitals.

4. ms is associated with the spin of the electron about its axis. ms can be

+1/2 or -1/2. If there are 2 electrons in the same orbital, one has to have ms = + ½ and

the other -1/2. Such electrons are said to be paired.

l (sublevel) / 0 / 1 / 2 / 3
Notation / s / p / d / f
# of orbitals (ml) / 1 / 3 / 5 / 7
Orbital notation / ( ) / ( ) ( ) ( ) / ( ) ( ) ( ) ( ) ( ) / ( ) ( ) ( ) ( ) ( ) ( ) ( )
Maximum #es / 2 / 6 / 10 / 14

Capacity of any level = 2n2 electrons where n = energy level

Level nTotal # of electrons in level

1 2

2 8

3 18

4 32

Discuss how this is order is related to the periodic table

Explain the use of periodic table in writing electronic configurations.

H = 1s1

He = 1s2

Li = 1s2 2s1

Be = 1s2 2s2

S = 1s2 2s2 2p6 3s2 3p4

Ni = 1s2 2s2 2p6 3s2 3p6 4s2 3d8

Hund's Rule: In an atom in which orbitals of equal energy (degenerate orbitals) are to be filled by electrons, the order of filling is such that as many electrons remain unpaired as much as possible.

Orbital Notation

S = 1s2 2s2 2p6 3s2 3p4

() () () ()() () ()()()

Li Be+ B2+ C3+ N4+ O5+ F6+

Each ion has 3 electrons and the following electron configuration: 1s2 2s1

They are said to be isoelectronic

Exercise: Write electronic configuration for Cl, Br, F.

Notice the number of electrons in the outermost shell in each atom is 7. These are called valence electrons. The number of valence electrons = the group # for the s and p block (representative) elements.

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