Quantum Numbers

•Four Quantum Numbers:

–Specify the “address” of each electron in an atom

–Used the wave equation to represent different energy states of the electrons

–Set of four #’s to represent the location of the outermost electron

Principal Quantum Number, n

This quantum number is the one on which the energy of an electron in an atom primarily depends. The smaller the value of n, the lower the energy level and the smaller the orbital.

The principal quantum number can have any positive value: 1, 2, 3, . . .

Orbitals with the same value for n are said to be in the same shell.

Energy Levels or Shells are sometimes designated by uppercase letters and related the principal quantum number as follows

Angular Momentum Quantum

 Number, l

This quantum number distinguishes orbitals of a given n

(shell) having different shapes.

It can have values from 0, 1, 2, 3, . . . to a maximum of (n – 

1).

For a given n, there will be n different values of l, or n 

types of subshells.

Orbitals with the same values for n and l are said to be in 

the same shell and subshell.

Orbit and Orbital

                 ORBIT

•It is well-defined circular path followed by electron around nucleus.

•It represents two dimensional motion of electron around nucleus.

•The maximum no. of electrons in an orbit is 2n2.

•Orbit is circular in shape.

                                                 ORBITAL

•It is a region of space around the nucleus where the probability of finding an electron is maximum.

•It represents three dimensional motion of electron around nucleus.

•The maximum no. of electrons in an orbital is 2.

•Orbitals have different shapes.

Bohr Atomic Model: Energy-Level Postulate

An electron can have only certain energy values, called energy levels. Energy levels are quantized.

For an electron in a hydrogen atom, the energy is given by the following equation:

                              E= -RH/ n^2

RH = 2.179 x 10-18 J (Rydberg constant)

n = principal quantum number

Bohr Atomic Model

•An electron could only orbit the nucleus in particular circular orbits with fixed angular momentum  and energy. Under this model an electron could not spiral into the nucleus because it could not lose energy in a continuous manner.

•Electron could make instantaneous “quantum leaps” between the fixed energy levels. When this occurred, light was emitted or absorbed at a frequency proportional to the change in energy, hence the absorption and emission of light in discrete spectra.