1 Atoms and Quantum Numbers GLY 4200 – Lecture 5 –Fall, 2015.

1

Atoms and Quantum Numbers

GLY 4200 – Lecture 5 –Fall, 2015

2

Atom

• Grossly oversimplified view of atom, but it does have a nucleus and electron cloud

3

Nucleons

• Protons – charge of +1

• Neutrons – neutral, with a mass slightly greater than the proton

• Atomic number = number of protons, often denoted z

• Atomic number is designated as a left subscript to the chemical symbol - 1H, 14Si

4

Atomic Weight

• The atomic weight equals the number of protons plus neutrons

• Atomic weight is shown as a left superscript to the chemical symbol, such as 16O

5

Isotopes

• One element may have one or more numbers of neutrons:

11H is normal hydrogen, with one proton and no

neutrons

12H is deuterium, or heavy hydrogen, with one proton

and one neutron

13H is tritium, a radioactive form of hydrogen, with one

proton and two neutrons

• Collectively, the different types of the atoms of one element are called isotopes

6

Ions

• Cation - the atom has lost electrons, so there is a net positive charge

• Anion - the atom has gained electrons, so there is a net negative charge

• Cations are found toward the left side and center of the periodic table, while anions are found on the right side

7

Planetary Model of the Atom

• Early models of the atom showed the electrons circling the nucleus like the planets orbit the sun

• Figure shows nitrogen represented this way

8

Johann Balmer

• Discovered a formula for the spectral lines of hydrogen in 1885

9

Neils Bohr• Danish physicist

• 1885-1962

• Formulated the next model of the atom, now called the Bohr model

• Won the 1922 Nobel prize for physics

10

Bohr Model of Nitrogen

• Electrons are in discrete orbitals • Two of the electrons are in the first energy level • The other five are in the second energy level

11

Spectral lines of Elements

12

De Broglie Waves

• An electron standing wave vibrating in an orbit around a nucleus of an atom

• Only integral numbers of wavelengths are allowed

13

Standing Wave, One Loop

• One String Vibrating, 1/2 wavelength • Two nodes• Quantum number n = 1

14

Standing Wave, Two Loops

• One String Vibrating, 1 wavelength • 3 nodes • Quantum number n = 2

15

Standing Wave, Four Loops

• One String Vibrating, 2 wavelengths • 5 nodes• Quantum number n = 4

16

Schrődinger’s Equation

17

Principal Quantum Number

• n has values 1,2,3.....• The Principal Quantum Number refers to

the angular momentum of the electron• n determines which shell of electrons is

being discussed May be referred to as n =1, n = 2, etc. In X-ray terminology, shells are assigned

letters, K,L,M,N,O,P,Q for n = 1 to 7

18

Azimuthal Quantum Number

• ℓ may take values 0, 1, 2, 3, ... (n-1)

• The Azimuthal Quantum Number Indicates the symmetry of the orbital

• ℓ determines the subshell to which an electron belongs s, p, d, f are used to designate ℓ = 0 to 3

19

Magnetic Quantum Number

• m has allowed values are 0, ±1, ±2, ±3, ..... ±ℓ

• The Magnetic Quantum Number refers to the orientation of the orbital in space

20

Spin Quantum Number

• s has allowed values are ±½

• The Spin Quantum Number refers to the direction of rotation of the electron itself

21

s Orbitals

• s orbitals are spherically symmetric

• The radius increases as n increases

• ℓ = 0

• One orbital, two electrons

22

p Orbitals

• p orbitals are aligned along the three principal axes• ℓ = 1• Three orbitals, six electrons

23

d Orbitals

• Four lobes, oriented as shown• ℓ = 2• Five orbitals, ten electrons

24

f Orbitals

• Complex shapes• ℓ = 3• Seven orbitals, fourteen electrons

25

Wolfgang Pauli

• Austrian physicist, 1900-1958

• Formulated the Exclusion Principle, which today bears his name

• Won the Noble Prize in Physics, 1945

26

Pauli Exclusion Principle

• Proposed in 1925

• The Pauli Exclusion Principle States that no two electrons in an atom can have the same four quantum numbers

• Since any given orbital has n, ℓ, and m the same, there can only be two electrons per orbital, with s = ±½