Made by :- Name :- Pranav Ghildiyal Class :- XI B

Classical mechanics, based on Newton’s laws of motion, successfully describes the motion of all macroscopic which have essentially a particle-like behaviour However it fails when applied to microscopic objects like electrons, atoms, molecules etc. This is mainly because of the fact that classical mechanics ignores the concept of dual

behaviour of matter especially for sub-atomic particles and the uncertainty principle. The branch of science that takes into account this dual behaviourof matter is called quantum mechanics.

Quantum mechanics is a theoretical science that deals with the study of the motions of the microscopic objects that have both observable wave like and particle like properties.

Quantum mechanics was developed independently in 1926 by Werner Heisenberg and Erwin Schrödinger. The fundamental equation of quantum mechanics was developed by Schrödinger and it won him the Nobel Prize in Physics in 1933. This equation which incorporates waveparticle duality of matter was proposed by de

Broglie

Types of Quantum NumbersTypes of Quantum Numbers

The principal quantum number ‘n’ is a positive integer with value of n = 1,2,3... .The principal quantum number determines the size and to large extent the energy of the orbital. For hydrogen atom and hydrogen like species (He + , Li, .... etc.) energy and size of the orbital depends only on ‘n’. The principal quantum number also identifies the shell.the increase in the value of ‘n’, the number of allowed orbital increases and are given by the following letters .

n = 1 2 3 4

Shell = K L M N .

Size of an orbital increases with increaseof principal Size of an orbital increases with increaseof principal quantum number ‘quantum number ‘n’. n’. Each shell consists of one or more Each shell consists of one or more sub-shellsor sub-levels. The number of sub-shellsin a sub-shellsor sub-levels. The number of sub-shellsin a principal shell is equal to the value value of n.For principal shell is equal to the value value of n.For example in the first shell (example in the first shell (n n = 1), there is only one sub- = 1), there is only one sub- shell which corresponds l = 0. Each sub-shell is shell which corresponds l = 0. Each sub-shell is assigned an azimuthal quantum number. Sub-shells assigned an azimuthal quantum number. Sub-shells corresponding to different values of corresponding to different values of l l are represented are represented in the following tablein the following table

Value for l 012345............

notation for sub-shell

spdf gh............

n L SubShell notations

1 0 1s

2 0 2s

2 1 2p

3 0 3s

3 1 3p

3 2 3d

4 0 4s

4 1 4p

4 2 4d

4 3 4f

Magnetic orbital quantum number. ‘m’ gives information about the spatial orientation of Magnetic orbital quantum number. ‘m’ gives information about the spatial orientation of the the

orbital with respect to standard set of co-ordinate axis. For any sub-shell (defined by ‘l’ orbital with respect to standard set of co-ordinate axis. For any sub-shell (defined by ‘l’ value) value)

2l+1 values of m are possible and these values are given by : m2l+1 values of m are possible and these values are given by : m1 1 = – l, – (l –1), – (l –2)... 0,1... = – l, – (l –1), – (l –2)... 0,1... (l – 2), (l–1), l.(l – 2), (l–1), l.

for l = 0, the only permitted value of mfor l = 0, the only permitted value of m l l = 0, [2(0)+1 = 1, one s orbital]. For can be –1, 0 and = 0, [2(0)+1 = 1, one s orbital]. For can be –1, 0 and +1 [2(1)+1 = 3, three orbitals]. For l = 2, m = –2, –1, 0, +1 and +2, [2(2)+1 = 5, five d orbitals]. It +1 [2(1)+1 = 3, three orbitals]. For l = 2, m = –2, –1, 0, +1 and +2, [2(2)+1 = 5, five d orbitals]. It should be noted that the values of mshould be noted that the values of m l l are derived from that the value of l are derived from are derived from that the value of l are derived from

n.n.

Value of l 0 1 2 3 4 5

Subshell notation s p d f g h

number of orbitals 1 3 5 7 9 11

In 1925, George Uhlenbeck and Sameul Goudsmit proposed the In 1925, George Uhlenbeck and Sameul Goudsmit proposed the presense of the fourth quantum number known as electron spin presense of the fourth quantum number known as electron spin quantum number. An electron spins around its own axis, much in a quantum number. An electron spins around its own axis, much in a Similar way as earth spins around its own axis while revolving Similar way as earth spins around its own axis while revolving

around around the sun. Spin angular momentum of the electron — a vector the sun. Spin angular momentum of the electron — a vector

quantity, quantity, can have two orientations relative to the chosen axis. These are can have two orientations relative to the chosen axis. These are

the two the two spin states of the electron and are normally represented by two spin states of the electron and are normally represented by two arrows, ↑ (spin up) and ↓ (spin down). Two electrons that have arrows, ↑ (spin up) and ↓ (spin down). Two electrons that have different different m m values (one+ and the other –) are said to have values (one+ and the other –) are said to have

opposite opposite spins. An orbital cannot hold more than two electrons and these spins. An orbital cannot hold more than two electrons and these

two two electrons should have opposite spins.electrons should have opposite spins.

‘‘n’ defines the shell, determines the size of the orbital and also to a n’ defines the shell, determines the size of the orbital and also to a large extent the energy of the orbital large extent the energy of the orbital

There are There are n subshells in the n subshells in the nnth th shell, ‘l’ identifies the subshell and shell, ‘l’ identifies the subshell and determines theshape of the orbital.There are (2determines theshape of the orbital.There are (2l+1) orbitals of each l+1) orbitals of each type in a type in a subshell, that is,one subshell, that is,one s orbital (l = 0), Three p orbitals (l = 1) s orbital (l = 0), Three p orbitals (l = 1) and five d orbitals (l = 2) and five d orbitals (l = 2) per subshell. To some extent ‘per subshell. To some extent ‘l’ also l’ also determines the energy of the orbital in a multi-electron atom.determines the energy of the orbital in a multi-electron atom.

MMl l designates the orientation of the orbital. For a given value of designates the orientation of the orbital. For a given value of l, l, m m has (2 has (2l+1) l+1) values, the same as the number of orbitals per subshell. values, the same as the number of orbitals per subshell. It means that the number of orbitals is equal to the number of ways in It means that the number of orbitals is equal to the number of ways in which they are oriented.which they are oriented.

MMs s refers to orientation of the spin of the electron. refers to orientation of the spin of the electron.

The orbital wave function or ψ for an electron in an atom has no physical meaning. It is simply a mathematical function of the coordinates of the electron. However, for different orbitals the plots of corresponding wave functions as a function of r (the distance from the nucleus) are different According to the German physicist, Max Born, the square of the wave function (ψ2 ) at a point gives the probability density of the electron at that point. For 1s orbital the probability density is maximum at thenucleus and it decreases sharply as we move

1s {n=1, l= 0 } 2s {n=2, l=0}

1s orbitals 2s orbitals

For 2p orbitalsFor 2p orbitals

For 3d orbitalsFor 3d orbitals

The filling of electrons into the orbitals of different atoms

takes place according to the aufbau principle which is based on the Pauli’s exclusion principle, the Hund’s

rule Of maximum multiplicity and the relative energies of

the orbitals.

The distribution of electrons into orbitals of an atom is called its electronic configuration. If one keeps in mind the basic rules which govern the filling of different atomic orbitals, the electronic configurations of different atoms can be written

very easily.