This theory was proposed by Hund and Mulliken in 1932. The basic idea of the theory is that atomic orbitals of individual atoms combine to form molecular orbitals.
Valency bond theory was proposed by Heitler and London in 1927 and it was further developed by Linus Pauling.
The basic idea of the theory are:
1. A covalent bond is formed by the overlap of half-filled atomic orbitals of the different atoms.
2. The overlapping atomic orbitals must have electrons with opposite spins.
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Electronic configuration of atoms using Aufbau, Pauli's principle and Hund's rule - Chemistry
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Elearin
Atomic orbitals are the sub-stationary states or the regions in space where the electrons revolve around the nucleus in an atom.
Electronic configuration of atoms is representation of the occupation of electrons in the orbitals. In other words, electronic configuration of atoms specifies the order in which electrons fill up the orbitals. The order in which these electrons are filled into the atomic orbitals are controlled by three principles.
According to this principle an electron always occupies the lowest energy orbital first before filling the higher level. For example, an electron always occupies 2s, the lower energy orbital, first instead of the higher 3s orbital.
The Aufbau or building-up principle can be explained with the example of Hydrogen Atom. Hydrogen has one electron. This electron enters the 1s orbital which has the lowest energy.
In other words, building-up principle states that the incoming electrons go to an orbital which has the least (n+l) value. However, the orbital having lower 'n' value will be occupied first, in case any two orbitals have the same (n+l) value.
Consider the example of Silicon whose atomic number is 14. Twelve electrons can be accommodated in 1s, 2s, 2p, 3s orbitals. Now, the last two electrons can enter into either 3p or 4s orbital. The (n+ l) values of these orbitals are the same, that is,
3p orbital has a (n+l) value of 3+1=4 and 4s has (n+l) value of 4+0 = 4
This means, both the orbitals have the same (n+l) value. But the 3p orbital has 'n' value, that is 3, which is less than the n value of 4s, which is 4. Therefore thirteenth and fourteenth electrons occupy the 3p orbital first. Thus the electronic configuration of Si is 3s2 3p2.The superscript represents the number of electrons present in the corresponding orbital.
The second important rule to determine the electronic configuration of an atom is the Hund's Rule. It says electron pairing happens only after all the available degenerate orbitals are occupied by one electron each.
Hund's rule example: . Consider the element Oxygen with Z=8. I has 8 electrons, the first electron goes into the '1s' orbital of the K-Shell. The second electron will be paired up with the first in the same 1s orbital. Similarly the third and fourth electrons will occupy the 2s orbital of L-Shell. The Fifth electron goes into one of the three 2p orbitals of L-Shell. Let that be 2px. Since the three p-orbitals i.e., 2px,2py and 2pz are degenerate , the sixth electron goes into 2py or 2pz but not 2px. Let us say it goes to 2py. Since 2pz is a degenerate orbital, the seventh electron goes to 2pz instead of pairing up with electron in 2px or 2py.
Now, since all the 3 sub-orbitals have one electron each, the eighth electron can pair up with any of the three electrons in 2px, 2py and 2pz orbitals. Thus the electronic configuration of Oxygen can be written as 1s1.2s2. 2px2 .2py1. 2pz1. The arrows indicate electrons with spin +1/2 and -1/2. Let us consider the nitrogen atom. it has 7 electrons. The first six electrons have the same arrangement as that of carbon atom 1s1.2s2. 2px1 .2py1. The seventh electron will enter only in 2pz but can not enter into 2px or 2py orbital. Thus the configuration is 1s1.2s2. 2px1 .2py1 2pz1
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The third important rule for electronic configuration, the Pauli's Exclusion Principle states that no two electrons will have the four quantum numbers same. This means that two electrons can ever have any identical values of n, l, m and s values. Because of this rule a single orbital can have only 2 electrons.
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1.7 Orbital Wave Functions and Shapes of Orbitals - Video Lectures
1.7 Orbital Wave Functions and Shapes of Orbitals
1. Spherical shape for s.
2. Dumbbell shape for orbitals of p.
3. Four-lobed shape for orbitals of d.
4. Complex shape for all orbitals of higher sublevels
The Wave Behavior of Matter (Part 1 of 2 for Atomic Orbitals)
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dcaulf
Atomic Orbitals Explained (Sequel to Wave Behavior of Matter)
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dcaulf
Shapes of Atomic Orbitals - IIT JEE Main and Advanced Chemistry Video Lecture
According to quantum mechanical model or wave mechanical model of atom, orbitals represent regions in space around the nucleus where the probability of finding electrons is maximum. A large number of orbitals are possible in an atom.
To describe each electron in an atom in different orbitals, four quantum numbers are used. They are designated as n,l,ml, and ms.
1. Principal quantum number (n) This quantum number determines the main energy shell or level in which the electron is present. It can have whole number values starting from 1 in an atom.
The principle quantum number indicates the average distance of the electron from the nucleus. If n = 1, it is closest to the nucleus and has lowest energy.
Eariest practice was to number shells as K,L,M,N etc.
Shell with principal quantum number n = 1 is called K.
Shell with principal quantum number n = 2 is called etc.
2. Azimuthal quantum number or angular quantum number (l): This number determines the angular momentum of the electron.
It can have positive integer values from zero to (n-1) where n is the principal quantum number. For each value of n, there are n possible values of l.
For n =3, l has three values: l = 0,1,2
The earlier practice is to designate l as subshell and refer it by letters s,p,d,f,….
l=0 = s; l=1=p; l=2=d, l=3=f etc.
The energy of subshell increases with increasing value of l.
3. Magnetic quantum number ( ml): Magnetic field acts on moving electrical charges. ( from chapters on magnetism in physics syllabus). On revolving electrons external magnetic field of the earth acts. Therefore, the electrons in a given subshell orient themselves in certain preferred regions space around the nucleus. These are called orbitals. This quantum number gives the number of orbitals for given angular quantum number l or in a given subshell.
The allowed values of ml are –l through 0 to +l.
There are (2l+1) values of ml for each value of l.
If l = 0, ml has only one value. ml = 0.
If l = 3, ml has 7 values.
ml = -3,-2,-1,0,1,2,3
4. Spin quantum number (ms) : It is observed that the electron in an atom is not only revolving around the nucleus but is also spinning around its own axis. This quantum number describes the spin orientation of the electron.
The electron can spin in two ways – clockwise and anticlockwise.
Values of +1/2 and -1/2 are given to this quantum number. Its value is not dependent on other quantum numbers.
The orientations of spin are also designated by up and down arrows ↑ ↓.
1.4 Wave Mechanical Model of Atom and Concept of Atomic Orbital - Video Lectures
1.4 Wave Mechanical Model of Atom and Concept of Atomic Orbital
Quantum mechanics or wave mechanics is a theoretical science which deals with the study of the motion of the microscopic objects (like electron) which have both observable wave like and particle like properties.
Quantum mechanics was developed indepdendently in 1926 by Werner Heisenberg and Erwin Schrodinger. In 1927, Schrodinger wave equation was published.
Atoms are the smallest particle of an element which may or may not have independent existence, but it takes part in chemical reactions.
Molecule is the smallest particle of a substance (element or compound) capable of independent existence.
There are 112 elements in nature as per the present knowledge. Obviously there are 112 different types of atoms.
Molecules may have two or more atoms. Molecules are divided into two types:
1. Homoatomic molecules
2. Heteroatomic molecules
1.10 Atomic and Molecular Mass
Atomic Mass: An atom is such a small particle that its mass cannot be determined with the help of any available balance. By an indirect method, the absolute mass of hydrogen atom has been found to be 1.66 X 10 to the power of -24 g.
Chemists have defined the atomic mass of hydrogen as one and expressed the atomic mass of other elements as multiples of hydrogen's atomic mass. The relative atomic masses expressed in terms of hydrogen as termed atomic weights.
Atomic weights of some common elements
Metals
Magnesium 24.3
Aluminium 27.0
Iron 55.8
Zinc 65.4
Tin 118.7
Gram Atomic Mass: Gram atomic mass is the quantity of an element whose mass in grams is numerically equal to its atomic mass.
Molecular Mass: Measuring the mass of a single molecule is not possible. Hence as in the case of atoms, molecular mass is defined as the average relative mass of its molecule as compared to the mass of an atom of carbon (C12) having mass number 12.
To provide theoretical justification to the laws of chemical combination which are experimentally verified, John Dalton postulated a simple theory of matter. The basic postulates of Dalton’s atomic theory are:
a. Matter is made up of extremely small indivisible and indestructible ultimate particles called atoms.
b. Atoms the same element are identical in all respects ie., in shape, size, mass and chemical properties.
c. Atoms of different elements are different in all respects and have different masses and chemical properties.
d. Atom is the smallest unit that takes part in chemical combinations.
d. Atoms of two or more elements combine in a simpler whole number ratio to form compound atoms (molecules).
e. Atoms can neither be created nor destroyed during any physical or chemical change.
f. Chemical reactions involve only combinations, separation or rearrangement of atoms.
Modern atomic theory
As a result of new discoveries made after Dalton developed his postulates, some modifications were done to atomic theory. They are:
1. Atom is no longer considered to be indivisible: It is found that atom is made up of subatomic particles such as electrons, protons and neutrons. We now state how many electrons are there, protons are there in an atom.
2. Atoms of same element may not be similar in all respects. Atoms of same elements have different atomic masses. These different atoms are called isotopes.
3. Atoms of different elements may have similar one or more properties. Atomic mass of calcium and argon (40 a.m.u.) are same. So the property of atomic mass is same for atoms of different elements. Isobars or elements or atoms having the same atomic mass.
4. Atom is the smallest unit which takes part in chemical reactions. Though electrons and protons are there, it is atom which takes part in chemical reactions and electrons exchange takes place between atoms.
5. The ratio in which the different atoms combine may be fixed and integral but may not always be simple. For example in sugar molecule the ratio of C,H and O atoms is 12:22:11, which is not simple.
6. Atom of one elements may be changed into atoms of other element. Transmutation is the process by which atoms one element can be changed into elements of other elements by subjecting it to alpha rays.
7. The mass of atom can changed into energy. Mass and energy are convertible. The equation give for such conversion is E = mc². Hence we cannot say that mass is not destructible. But in chemical reactions, atom remains unchanged and its mass is not destroyed to liberate energy.
1.3 Heisenberg's Uncertainty Principle - Video Lectures
Heisenberg's Uncertainty principle
In 1927, Heisenberg put forward a principle known as Heisenberg’s uncertainty principle.
According it, “it is not possible to measure simultaneously both the position and momentum (or velocity) of a microscopic particle, with absolute accuracy.”
Mathematically, this principle is expressed as:
∆x * ∆p = h/4 π
Where
∆x = uncertainty in position
∆p = uncertainty in momentum
The constancy of the product of uncertainties means that, if the position of the particle is known with more accuracy, there will be large uncertainty in momentum and vice versa.
This uncertainty arises, as all observations are made by impact of light, the microscopic objects suffer a change in position or velocity as a result of impact of light. So there is a disturbance in them due to the measurement.
The principle does not affect the measurement of large objects as in these cases impact of light does not created any appreciable change in their position or velocity.
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AK Lectures
Heisenberg Uncertainty Principle Example # 1
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a. Law of conservation of mass
During any physical or chemical change, the total mass of the products is equal to the total mass of reactants.
b. Law of constant proportions
A pure chemical compound always contains same elements combined together in the same definite proportion by weight.
c. Law of multiple proportions
When two elements combine to form two or more than two compounds, the weights of one of the elements which combine with a fixed weight of the other, bear a simple whole number ratio.
d. Law of reciprocal proportions
When two different elements combine separately with the same weight of a third element, the ratio in which they do so will be the same or some simple multiple of the ratio in which they combine with each other.
e. Gay Lussac’s law of combing volumes
Under similar conditions of temperature and pressure, whenever gases react together, the volumes of the reacting gases as well as products (if gases) bear a simple whole number ratio.
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1.5 Chemical Classification of Matter - Video Lectures
1.5. Chemical classification of matter
1. Element
Further classification: Metals, non-metals, metalloids
2. Compound
Further classification: Inorganic and organic
3. Mixture
Further classification: Homogeneous mixtures - they are called solutions.
Heterogeneous mixtures: They have visible boundaries of separation between the different constituents and they can be easily seen with naked eye.
Video Lectures 1.4 Measurement and Significant Figures
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Issacs Teach
Accuracy
Accuracy is a measure of the difference between the true value (the value to be measured) and the value measured by an instrument.
Precision is depends totally on the instrument and it is the difference between measurements of the same dimension made number of times. It is expressed as the difference between one measurement and the arithmetic mean of the number of measurements.
Significant figures: Significant figures in a number are include all the certain digits plus one doubtful digit.
If a number has 4 significant figures or digits, it means 3 of them are certain and fourth one is doubtful.
Rules for determining the number of significant figures
1. All non-zero digits are significant
Decimal place does not determine the number of significant figures.
2. A zero becomes significant in case it comes between two non-zero numbers.
3. The zeros at the beginning of a number are not significant.
For example 0.0004 has only one significant figure.
4. All zeros placed to right of a number are significant. They represent the precision of the measuring scale.
For example 267.000 has six significant figures.
(The precision does not come by writing the number. It comes because the instrument has the ability to read a number certainly up to that level of measurement.)
Rules of calculations involving significant figures
Rule 1. The final result of addition or subtraction should be reported up to the same number of decimal places as are present in the term having the least number of decimal places.
Example- addition of three numbers
6.414
2.3
0.501
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9.215 is the answer but the answer should be reported up to one decimal place only as 2.3 is the term having least number of decimal places.
Hence correct answer is 9.2
Rule 2. In multiplication or division, the final result should be reported up to the same number of significant figures as are present in the term with the least number of significant figures.
Example: 4.2345*1.25 = 5.293125
The final result should be reported up to three significant figures only as 1.25 has three significant figures. Hence the correct answer to be reported is 5.29.
Rounding off figures of retention of significant figures.
i) If the digit coming after the desired number of significant figures happens to be more than 5, the preceding digit or figure is increased by 1.
ii) If that digit is less than 5, it is neglected and hence the preceding significant figure remains unchanged.
iii) If that digit happens to be 5, the preceding digit is increased by one in case it is odd number. If preceding digit is an even number, it remains the same.
If the problem has number of steps, the rounding off is to be done at the final answer level only.