Sunday, October 21, 2007


JEE Syllabus

Atomic structure and chemical bonding:
Bohr model, spectrum of hydrogen atom, quantum numbers;
Wave-particle duality, de Broglie hypothesis;
Uncertainty principle;
Quantum mechanical picture of hydrogen atom (qualitative treatment), shapes of s, p and d orbitals;
Electronic configurations of elements (up to atomic number 36);
Aufbau principle;
Pauli's exclusion principle and Hund's rule;

Main topics in TMH Book Chapter


In 1913, Niels Bohr proposed a model of the atom. He proposed that the electrons in an atom could only be in certain orbits, or energy levels, around the nucleus. Refinement of Bohr theory led to the modern theory of atomic structure based on quantum mechanics. The energy levels proposed by Bohr were calculated and it was further modeled that each energy level or orbit has sublevels and each sublevels has one or more orbitals.
Orbit - sublevel – Orbital

Electrons are moving around the nucleus and orbitals represent a space where a pair of electrons is most likely to be found. This means that electrons may sometimes go out of the orbital but most of the time they are found in the orbital.

The quantum mechanics calculations gave out the result that there is a limit to the number of electrons that can occupy a given orbit or energy level.


The orbits are called as shells. The energy level of orbits or shells increases as they increase in distance from the nucleus of the atom. The orbits or shells are represented by numbers as 1,2,3,4,5,6 or 7. They are represented by letters as K,L,M,N,O,P,Q.

It is found that the maximum number of electrons in each energy level is equal to 2n2 where n is the number of energy level.

Therefore energy level 1 will have 2 electrons.
Energy level 2 will have 2*4 = 8 electrons
Energy level 3 will have 2*9 = 18 electrons.

Sublevel of an Orbit

The energy levels, or orbits or shells are further divided into sublevels, or subshells. These subshells are designated by letters: s for the first possible sublevel, p for the second possible sublevel, d for the third, f for the fourth, g for the fifth, and from here on they simply go in alphabets.

The number of sublevels of each energy level is equal to the number of the energy levels. This means energy level 1, the K shell will have only one sub levels – s sublevel. The energy level 2, the L shell will have 2 sub levels – s and p.


Sublevels have further divisions called orbitals. Electrons are found in these orbitals. Each orbital contains two electrons.

“s” sublevel has only one orbital. “p” sublevel has 3 orbitals. “d” sublevel has 5 orbitals. “f” sublevel has 7 orbitals.

As each orbital can hold two electrons, orbitals of s can hold two electrons. The orbitals are of p sublevel are named as px and py and pz. The orbitals of p contain 6 electrons. The orbitals of d are 5. The orbitals of d are named as dxy, dxz,dyz,dx2-y2 and dz2. The d sublevel orbitals contain 10 electrons.

The two electons in each orbital spin in different directions.

Shape of Orbitals

Each type of orbital( s, px and py and pz, dxy, dxz,dyz,dx2-y2 and dz2 ) has a unique shape.

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.

Electron Structure or Configuration

In the orbital-sub level-orbit structure, energy level of orbit 1 is less than that of 2 and so on. In each orbit, the sublevel s if of lower energy than the p sublevel, and p is of lower energy than the d sublevel and so on. Orbital of a sublevel are all of equal energy.

Electrons occupy the lowest energy sublevels that are available. This is known as ‘aufbau’ order or principles. In the case of an atom having atomic number of 1, the lone electron occupied the s orbital of sublevel s of orbit 1(represented as 1s1). In case of an atom having atomic number 3 the electrons first occupy the sublevel of orbit 1(this can hold only two electrons) and then occupy p sublevels of orbit 2 (represented as 1s2,2s1).

Hund’s rule says that, for any set of orbitals of equal energy say p orbitals of orbit 2, there is one electron is each orbital before the second electron enters or occupies an orbital.
The energy level of some sublevels at higher orbits is less than the some sublevels at lower orbitals. This fact is to be kept in mind when electron configuration is determined for any atom. The increasing order of energy levels of sublevels is:

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f*, 5d, 6p, 7s, 5f*, 6d, 7p, 8s

* In this case one electron one electron goes into 5d and then 4f fills completely and then rest of 5d. Similar thing happens in 5f and 4d.

Atomic particles are said to have spin. What does that imply?

A good explanation for electron spin is provided by
Spin is an intrinsic property of an electron, like its mass or charge. In elementary treatments, spin is often visualized as an actual spinning motion. However, it is a quantum mechanical property without a classical counterpart, and to picture spin in this way can be misleading. Nevertheless, for the present discussion, such a picture is useful. An electron has a fixed amount of spin, in the sense that every electron in the universe is continually spinning at exactly the same rate. Although the spin of an electron is constant, the orientation of the axis of spin is variable, but quantum mechanics restricts that orientation to only two possibilities. The two possible spin states of an electron are represented by the arrows and and are distinguished by the spin magnetic quantum number, ms, which takes the values +1/2 (for the spin) or -1/2 (for the spin). Because of its spin, an electron must obey a fundamental requirement known as the Pauli exclusion principle. This principle (which is a consequence of the more fundamental Pauli principle; see the article atom: Electrons) states that no more than two electrons may occupy a given orbital and, if two electrons do occupy one orbital, their spins must be paired (denoted ; that is, one electron must be and the other must be ). The Pauli exclusion principle is responsible for the importance of the electron pair in the formation of covalent bonds. It is also, on a more cosmic scale, the reason why matter has bulk; that is to say, all electrons cannot occupy the orbitals of lowest energy but are instead located in the many shells that are centred on the nucleus. Also owing to the existence of spin, two objects do not simply blend into one another when they are in contact; the electrons of adjacent atoms cannot occupy the same space, thereby prohibiting the combining of two atoms into one. Here again is an example of a seemingly trivial property, in this case spin, having consequences of profound and macroscopic importance. In this instance, the spin of the electron is responsible for the existence of identifiable forms of matter.


web sites
Atomic Structure, Isotopes, Periodic Table and Electronic Structure of Atoms

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