Transcript 30-32: Main Topics

28-30
• Ch.28:
Read Section 1
• Ch.29:
4, 7, 27, 41.
• Ch.30:
Read Sections 1-3.
1
Matter Waves
• DeBroglie: l = h/(mv), noticeable for small
momentum, e.g. electron
Ex. Electron, v = 4000m/s:
l = (6.63x10-34 Js)/[(9.1x10-31kg)(4000m/s)] = 0.182 um
2
stationary states
• DeBroglie: electron orbits are integral
multiples of the matter wavelength
nl  2r
r
3
Rutherford Scattering
• positive radiation on metal foil
• Video simulation
• Uniform positive solid would cause
similar deflections
• actual result: wide variation
• Conclusions:
• Solid not uniform
• But have small +nuclei
4
symbols
•
•
•
•
Z = Atomic Number = #p
A = Mass Number = #p + #n
X = Element Symbol
full symbolic form: A X
Z
• Example: Helium =
4
2
He
5
radioactivity
•
•
•
•
•
“alpha” (helium nucleus)   He

“beta” (electron)   e
“gamma” (photon) 
thickness of lead required to shield:
alpha (~0.01mm), beta (~0.1mm), gamma
(~100mm)
4
2
6
Activity & Decay
•
•
•
•
•
Decay: A  B + radiation
Half-life: time when half of A remains
Activity ~ Decay rate
Activity large when half-life small
Activity small when half-life large
7
Radiation parameters
• N = number of atoms
• l = decay constant
N  N oe
 lt
• T1/2 = half-life
• T1/2 = 0.693/ l.
• Activity = -lN
8
Example 1
• Given No = 32,000, half-life = 1.5 days.
• Calculate N after 4.5 days
•  l = 0.693/T1/2. = 0.693/1.5days.
N  Noe
 lt
 (32,000)e
 ( 01..693
) 4.5 d
5d
 4001
9
Alternate Formula
NN

1 ( t / T1 / 2 )
o 2
• Given No = 32,000, half-life = 1.5 days.
• Calculate N after 4.5 days
N  32,000

1 ( 4.5d /1.5d )
2
 32,000

1 3
2
 4,000
10
Example 2
• Given No = 64,000, half-life = 44 min.
• Calculate N after 5 hours (300min.)
N  64,000

1 ( 300min/ 44 min)
2
 567
11
nuclear stability
•
•
•
•
regulated by neutrons
higher Z atoms are less stable
Z = 83 (Bismuth) largest stable atom
Z >= 84 (Polonium) are unstable
(radioactive)
12
nuclear binding energy
•
•
•
•
mass atom < mass of parts
difference is called “mass defect”
binding energy ~ mass defect
Shifts to more stable states release
energy, e.g. book falls over
• Fission: broken atoms more stable
• Fusion: joined atoms more stable
• Fission simulation
13
End
14
nuclear transformations
• alpha: Z reduced by 2, A reduced by 4
• beta: Z increases by 1, A stays same
• examples:
U  Th  He
238
92
234
90
4
2
Th Pa e
234
90
234
91
0
1
15
Light Photon
• Smallest amount of EM wave
• Carries energy and momentum
• constant h is “Planck’s” Constant


hc  4.1357 1015 eV  s 2.9979 108 m / s

hc 1240eV  nm
16
Uncertainty in p, E
• Limiting one variable causes another
variable to become more uncertain.
• Heisenberg Uncertainty Principle
py  h 4
Et  h 4
17
Photon Momentum
• p = h/l
• SI units: h = 6.63x10-34 J·s
Ex. momentum of a photon with wavelength 130 nm:
p = h/l = (h = 6.63x10-34 J·s)/(130x10-9m) = 5.1x10-27 kg·m/s
[J·s/m = N·m·s/m = N·s = kg·m/s]
18
Electron Theories
• Electrons determine physical properties
including:
• resistivity
• hardness
• light emission and absorption
19
quantum mechanical picture
• involves 4 quantum numbers (3 more than
the Bohr model)
• quantum-mechanical model allows for
electron states with zero angular
momentum
20
electron shell theories
• electrons in stable ‘orbits’
• collisions cause electron
“planets” to move to larger,
higher energy, orbits
• “light” energy emitted when they
drop back to their original
smaller orbits
21