Upload
nomio0703
View
700
Download
0
Embed Size (px)
DESCRIPTION
Citation preview
Physics 102: Lecture 25, Slide 1
Periodic Table, Atomic Structure
Physics 102: Lecture 25
Physics 102: Lecture 25, Slide 2
From last lecture – Bohr model
2 4 2 2
2 2 2
13.6 eV where / 2
2n
mk e Z ZE h
n n
2 2 2
2
10.0529 nm
2n
h n nr
mke Z Z
Ln = nh/2π
Angular momentum is quantized
Energy is quantized
Radius is quantized
n = 1, 2, 3 ...
Linear momentum too Bohr model is incorrect!
Physics 102: Lecture 25, Slide 3
Quantum NumbersEach electron in an atom is labeled by 4 #’s
n = Principal Quantum Number (1, 2, 3, …)• Determines energy (Bohr)
ms = Spin Quantum Number (-½ , +½)
• “Up Spin” or “Down Spin”
l = Orbital Quantum Number (0, 1, 2, … n-1)
• Determines angular momentum• l < n always true!
ml = Magnetic Quantum Number (-l , … 0, … l )
• Component of l • | ml | <= l always true!
( 1)2
hL
2z
hL m
Note differences with Bohr model
Physics 102: Lecture 25, Slide 4
ACT: Quantum numbers
For which state of hydrogen is the orbital angular momentum required to be zero?
1. n=1
2. n=2
3. n=3
Physics 102: Lecture 25, Slide 5
l =0 is “s state”
l =1 is “p state”
l =2 is “d state”
l =3 is “f state”
l =4 is “g state”
1 electron in ground state of Hydrogen:
n=1, l =0 is denoted as: 1s1
n=1 l =0 1 electron
Spectroscopic Nomenclature “Subshells”“Shells”
n=1 is “K shell”
n=2 is “L shell”
n=3 is “M shell”
n=4 is “N shell”
n=5 is “O shell”
Physics 102: Lecture 25, Slide 6
Electron orbitalsIn correct quantum mechanical description of atoms, positions of electrons not quantized, orbitals represent probabilities
Physics 102: Lecture 25, Slide 7
Quantum Numbers
How many unique electron states exist with n=2?
l = 0 :ml = 0 : ms = ½ , -½ 2 states
l = 1 :ml = +1: ms = ½ , -½ 2 states
ml = 0: ms = ½ , -½ 2 states
ml = -1: ms = ½ , -½ 2 states
2s2
2p6
There are a total of 8 states with n=2
Physics 102: Lecture 25, Slide 8
ACT: Quantum NumbersHow many unique electron states exist with n=5 and ml = +3?
A) 0 B) 4 C) 8 D) 16 E) 50
Physics 102: Lecture 25, Slide 9
Preflight 25.2
What is the maximum number of electrons that can exist in the 5g (n=5, l =4) subshell of an atom?
Physics 102: Lecture 25, Slide 10
In an atom with many electrons only one electron is allowed in each quantum state (n, l, ml, ms).
Pauli Exclusion Principle
This explains the periodic table!
Physics 102: Lecture 25, Slide 11
Atom Configuration H 1s1
He 1s2
Li 1s22s1
Be 1s22s2
B 1s22s22p1
Ne 1s22s22p6
1s shell filled
2s shell filled
2p shell filled
etc
(n=1 shell filled - noble gas)
(n=2 shell filled - noble gas)
Electron Configurations
p shells hold up to 6 electronss shells hold up to 2 electrons
Physics 102: Lecture 25, Slide 12
s (l =0)
p (l =1)
d (l =2)
f (l =3)
n =
1,
2,
3,
...
The Periodic Table
What determines the sequence?Pauli exclusion & energies
Also s
Physics 102: Lecture 25, Slide 13
2s electrons can get closer to nucleus, which means less “shielding” from the 1s electrons
Shell OrderingWhy do s shells fill first before p?
r
2p
P(r)
r
2s
P(r)1s1s
Physics 102: Lecture 25, Slide 14
Sequence of shells:
4s electrons get closer to nucleus than 3d
Sequence of Shells
1s2s 2p3s 3p 3d4s 4p 4d 4f5s 5p 5d 5f6s 6p 6d ...
1s,2s,2p,3s,3p,4s,3d,4p,
Pneumonic:
...
Physics 102: Lecture 25, Slide 15
Properties of elementsWe can understand the different properties of elements from the periodic table
Noble gases• Filled outer p-shell (s for He)• Hard to ionize• Non-reactive
Alkali metals• Unpaired outer s-shell e–
• Easy to ionize• Very reactive
Transition metals• Filling d-shell (l = 2)• Tend to be magnetic
s2p6 s1
d1 – d10
Physics 102: Lecture 25, Slide 16
Transition elements
Recall torque on current loop from B-field: = IABsin()
IA = -ep/(2rm) (r2) = -(e/2m)rp = -(e/2m)L
T = 2r/v = 2r/v = 2rm/p
In 3d shell we are putting electrons into l = 2; all atoms in middle are strongly magnetic. Why?
High angular momentum
Strongly magnetic!
Use Bohr model: Ze
e–
This looks like a current loop!
I
I = -e/T A = r2
r
Angular momentum!
Physics 102: Lecture 25, Slide 17
Yellow line of Na flame test is 3p 3s
Na 1s22s22p6 3s1
Neon - like core
Many spectral lines of Na are outer electron making transitions
Single outer electron
Sodium
www.WebElements.com
Physics 102: Lecture 25, Slide 18
Summary
• Each electron state labeled by 4 numbers:n = principal quantum number (1, 2, 3, …)
l = angular momentum (0, 1, 2, … n-1)
ml = component of l (-l < ml < l)
ms = spin (-½ , +½)
• Pauli Exclusion Principle explains periodic table
• Shells fill in order of lowest energy.