chemistry

QUANTUM NUMBERS

To fully explain the motion of electron and to locate it's correct address the following four

quantum numbers are required.

Principal quantum number (n) :

It is proposed by Bohr and denoted by 'n'.

It represents the main energy level.

It determines the size of the orbit and energy of the electron.

It takes all positive and integral values from 1 to n.

The maximum number of electrons in a main energy level is 2n2, and number of orbitals is n2.

As the value of 'n' increases, the energy of electron increases.

The energy of electron in the ground state of hydrogen atom is – 13.6 eV/atom(or) –2.176 x10–11

erg per atom(or) –2.176 × 10–18 joule per atom(or) –1312 kJ per mole (or) –313.6 kcal per mole.

The energy of the electron in the second orbit of hydrogen atom is

= – 22

13.6

= –3.4 eV/atom

Azimuthal quantum number  ( l ):

It is also known as angular momentum quantum number or orbital quantum number (or) subsidiary

quantum number.

To express the quantised values of the orbital angular momentum, azimuthal quantum number was

proposed.

It is denoted by 􀁁 and takes values from 0 to n – 1.

The number of values of ‘  ’ is equal to the value of n.

It explains fine structure in H-spectrum.

It determines the shape of orbitals.

More fine lines in each main spectral line are seen.

If n = 1, 􀁁 = 0 (s - sub-shell)

If n = 2, 􀁁 = 0, 1 (s, p sub-shells)

If n = 3, 􀁁 = 0, 1, 2 (s, p, d sub-shells)

If n = 4, 􀁁 = 0,1, 2, 3 (s, p, d, f - sub-shells)

Azimuthal quantum number determines the shape of the orbital.

The number of orbitals in a sub shell is (2 􀁁 + 1).

The maximum number of electrons in a sub shell is 2(2 􀁁 + 1).

Magnetic quantum number (m):

To explain Zeeman and Stark effects Lande proposed magnetic quantum number.

It is denoted by m.

It represents the sub-sub energy level or atomic orbital.

It determines the orientation of orbital in space.

When the atom is placed in an external magnetic field, the orbit changes its orientation.

The number of orientations is given by the values of the magnetic quantum number m.

m takes the values form – to + through 0. Total values of m for a given value of = (2 + 1) values.

A sub shell having azimuthal quantum number ℓ, can have (2 + 1) space orientations.

The number of orbitals in a subsheII = (2 + 1).

If the changes in the axis in one direction are indicated by + m values, the changes in the axis in the opposite direction are indicated by – m.

Spin quantum number (s):

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In the fine spectrum of alkali metals pairs of widely separated lines are observed which are different from duplet, triplet, and quadruplets observed in the hydrogen spectrum.

To recognise and identify these pairs of lines Goudsmit and Uhlenbeck proposed that an electron rotates or spins about its own axis.

This results in the electron having spin angular momentum, which is also quantised.

The electron may spin clockwise or anti clockwise. Therefore, the spin quantum number takes two values +1/2 and –1/2. Clockwise spin or parallel spin is given +1/2 or ↑ and anti clockwise or anti parallel spin is given by –1/2 or ↓.