Chapter 7: Quantum Mechanical Model of Atom

CHE 123: General Chemistry IDr. Jerome Williams, Ph.D.

Saint Leo University

Overview

• Bohr Model of Hydrogen Atom• Quantum Mechanical Model of Atom• Quantum Numbers

Bohr Model of Hydrogen Atom

• Niels Bohr - described atom as electrons

circling around a nucleus and concluded that

electrons have specific energy levels.

• Limited only to Hydrogen atom or Hydrogen

like ion.

Bohr Model of Hydrogen Atom

• Energy levels evaluated using the following equation

• E = -2.178 x 10-18 J (Z2 / n2)

• ΔE = E (final) – E (initial) = -2.178 x 10-18 J [ (1 / nfinal2 – 1 / ninital

2) ]

Quantum Mechanical Model of Atom

• Erwin Schrödinger - proposed quantum

mechanical model of atom, which focuses on

wavelike properties of electrons.

Quantum Mechanical Model of Atom

• Werner Heisenberg - showed that it is impossible to

know (or measure) precisely both the position and

velocity (or the momentum) at the same time.

• The simple act of “seeing” an electron would change

its energy and therefore its position.

Quantum Mechanical Model of Atom

• Erwin Schrödinger - developed a compromise which

calculates both the energy of an electron and the

probability of finding an electron at any point in the

molecule.

• This is accomplished by solving the Schrödinger

equation, resulting in the wave function, .

Quantum Numbers

• Wave functions describe the behavior of electrons.

• Each wave function contains three variables called quantum

numbers:

– • Principal Quantum Number (n)

– • Angular-Momentum Quantum Number (l)

– • Magnetic Quantum Number (ml)

Quantum Numbers

• Principal Quantum Number (n): Defines the size and energy level of the orbital. n = 1, 2, 3,

• As n increases, the electrons get farther from the nucleus.

• As n increases, the electrons’ energy increases.

• Each value of n is generally called a shell.

Quantum Numbers

• Angular-Momentum Quantum Number (l): Defines the three-dimensional shape of the orbital.

• For an orbital of principal quantum number n, the value of l can have an integer value from 0 to n – 1.

• This gives the subshell notation:l = 0 = s - orbital l = 1 = p - orbital

l = 2 = d - orbital l = 3 = f - orbital l = 4 = g - orbital

Quantum Numbers• Magnetic Quantum Number (ml): Defines the spatial

orientation of the orbital.

• For orbital of angular-momentum quantum number, l, the value of ml has integer values from –l to +l.

• This gives a spatial orientation of:

l = 0 giving ml = 0

l = 1 giving ml = –1, 0, +1

l = 2 giving ml = –2, –1, 0, 1, 2, and so on…...

Quantum Numbers

Quantum Numbers

• Why can’t an electron have the following quantum numbers?– (a) n = 2, l = 2, ml = 1 (b) n = 3, l = 0, ml = 3

– (c) n = 5, l = –2, ml = 1

• Give orbital notations for electrons with the following quantum numbers:– (a) n = 2, l = 1, ml = 1 (b) n = 4, l = 3, ml = –2

– (c) n = 3, l = 2, ml = –1

Quantum Numbers

• Spin Quantum Number (ms):

• The Pauli Exclusion Principle

states that no

two electrons can have

the same four quantum

numbers.