Material since exam 3

1
Material since exam 3

• De Broglie wavelength, wavefunctions,
  probabilities
• Uncertainty principle
• Particle in a box
• Wavefunctions, energy, uncertainty relation
• 1D, 2D, and 3D box, wavefunctions, energy
• 3D hydrogen atom
• Quantum s, physical meaning of quantum s
• Energies and wavefunctions
• Orbital magnetic dipole moment, electron spin
• Multielectron atoms
• State energies, electron configuration, periodic
  table
• Lasers
• Nuclear physics
• Isotopes, nuclear binding energy
• Radioactive decay
• Decay rates, activity, radiation damage
• Types of decay, half-life, radioactive dating.

2
Matter waves

• If light waves have particle-like properties,
  maybe matter has wave properties?
• de Broglie postulated that the wavelength of
  matter is related to momentum as
• This is called the de Broglie wavelength.

Nobel prize, 1929
3
Matter Waves

• deBroglie postulated that matter has wavelike
  properties.
• deBroglie wavelength

Example Wavelength of electron with 10 eV of
energy Kinetic energy
4
Heisenberg Uncertainty Principle

• Using
• ?x position uncertainty
• ?p momentum uncertainty
• Heisenberg showed that the product
• ( ?x ) ? ( ?p ) is always greater than ( h /
  4? )
• Often write this as
• where is pronounced h-bar

Plancksconstant
5
The wavefunction

• Particle has a wavefunction ?(x)

?2
?
?2(x)
x
x
dx
Very small x-range
probability to find particle in infinitesimal
range dx about x
Larger x-range
probability to find particle between x1 and x2
Entire x-range
particle must be somewhere
6
Question
?2
0.5nm-1

• What is probability that particle is found in
  0.01nm wide region about -0.2nm?

x
0

1. 0.001
2. 0.005
3. 0.01
4. 0.05
5. 0.1

-0.8nm
-0.2nm
About what is probability that particle is in the
region -1.0nmltxlt0.0nm?

1. 0.1
2. 0.4
3. 0.5
4. 1.5
5. 3.0

7
Particle in 1D box
n
Wavefunction
Probability
n3
n2

• n1

8
Particle in box energy levels

• Quantized momentum
• Energy kinetic
• Or Quantized Energy

nquantum number
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3-D particle in box summary

• Three quantum numbers (nx,ny,nz) label each state
• nx,y,z1, 2, 3 (integers starting at 1)
• Each state has different motion in x, y, z
• Quantum numbers determine
• Momentum in each direction e.g.
• Energy
• Some quantum states have same energy

10
Question

• How many 3-D particle in box spatial quantum
  states have energy E18Eo?
• A. 1
• B. 2
• C. 3
• D. 5
• E. 6

11
Q ask what state is this?
(121)
(112)
(211)
All these states have the same energy, but
different probabilities
12
3D hydrogen atom
For hydrogen atom

• n describes energy of orbit
• l describes the magnitude of orbital angular
  momentum
• m l describes the angle of the orbital angular
  momentum
• ms describes the angle of the spin angular moment

13
Other elements Li has 3 electrons
n2 states, 8 total, 1 occupied
n1 states, 2 total, 2 occupiedone spin up, one
spin down
14
Question

• Inert gas atoms are ones that have just enough
  electrons to finish filling a p-shell (except for
  He). How many electrons do next two inert gas
  atoms after helium ( neon (Ne) and argon (Ar) )
  have.
• In this range of atomic number the subshells fill
  in order of increasing angular momentum.

1. 10 18
2. 4 8
3. 8 16
4. 12 20
5. 6 10

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Multi-electron atoms

• Electrons interact with nucleus (like hydrogen)
• Also with other electrons
• Causes energy to depend on l

States fill in order of energy
1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d
Energy depends only on n
Energy depends on n and l
16
The periodic table

• Atoms in same column have similar chemical
  properties.
• Quantum mechanical explanation similar outer
  electron configurations.

Na3s1
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Electron Configurations
Atom Configuration
H 1s1
He 1s2
1s shell filled
(n1 shell filled - noble gas)
Li 1s22s1
Be 1s22s2
2s shell filled
B 1s22s22p1
etc
(n2 shell filled - noble gas)
Ne 1s22s22p6
2p shell filled
18
Ruby laser operation
3 eV
2 eV
Metastable state

• PUMP

1 eV
Ground state
19
Isotopes
Total nucleons
protons

• Carbon has 6 protons, 6 electrons (Z6) this
  is what makes it carbon.
• Most common form of carbon has 6 neutrons in the
  nucleus. Called 12C

• Another form of carbon has 6 protons, 8 neutrons
  in the nucleus. This is 14C.

This is a different isotope of carbonIsotopes
same protons, different neutrons
20
Nuclear matter

• Any particle in nucleus, neutron or proton, is
  called a nucleon.
• A is atomic mass number
• Atotal number of nucleons in nucleus.
• Experimental result
• All nuclei have same (incredibly high!) density
  of 2.3x1017kg/m3
• Volume ?A number of nucleons
• Radius ? A1/3

21
Binding energy

• Calculate binding energy from masses

Atomic masses well-known-gt easier to use
22
Biological effects of radiation

• Radiation damage depends on
• Energy deposited / tissue mass (1 Gy (gray)
  1J/kg)
• Damaging effect of particle (RBE, relative
  biological effectiveness)

Radiation type RBE X-rays 1Gamma rays 1Beta
particles 1-2Alpha particles 10-20

• Dose equivalent (Energy deposited / tissue
  mass) x RBE
• Units of Sv (sieverts) older unit rem, 1
  rem0.01 Sv
• Common units mSv (10-3Sv), mrem (10-3rem)
• Common safe limit 500 mrem/yr (5 mSv/yr)

23
Exposure from 60Co source

• 60Co source has an activity of 1 µCurie
• Each decay 1.3 MeV photon emitted
• Hold in your fist for one hour
• all particles absorbed by a 1 kg section of your
  body for 1 hour
• Energy absorbed in 1 kg

1. 0.5 rem
2. 0.3 rem
3. 0.1 rem
4. 0.05 rem
5. 0.003 rem

What dose do you receive?
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Quantifying radioactivity

• Decay rate r (Units of s-1)
• Prob( nucleus decays in time ?t ) r ?t
• Activity R (Units of becquerel (1 Bq1 s-1)
  or curie (1 Ci3.7x1010 s-1)
• Mean decays / s rN, N nuclei in
  sample
• Half-life t1/2 (Units of s)
• time for half of nuclei to decay t1/2

25
Activity of Radon

• 222Rn has a half-life of 3.83 days.
• Suppose your basement has 4.0 x 108 such nuclei
  in the air. What is the activity?

We are trying to find number of decays/sec. So we
have to know decay constant to get RrN
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Decay summary

• Alpha decay
• Nucleus emits He nucleus (2 protons, 2 neutrons)
• Nucleus loses 2 protons, 2 neutrons
• Beta- decay
• Nucleus emits electron
• Neutron changes to proton in nucleus
• Beta decay
• Nucleus emits positron
• Proton changes to neutron in nucleus
• Gamma decay
• Nucleus emits photon as it drops from excited
  state