Transcript Document

Photoelectric Effect
I
I0
Light
e
V0
–
A
f0
V
0
0
Current depends on potential; max current I0 (saturation) for high voltages.
 I0 reached when all electrons are collected
Positive current even for (small) negative potential up to V0 (“stopping potential”).
 V0 corresponds to max. Ekin: eV0 = Ekin, max
I0 (= # of electrons per time) depends on light intensity but NOT on frequency
V0 depends on the material and frequency, but not on intensity.
Emission only occurs for frequencies f > f 0 (V0 (f 0) = 0 )
The current is always observed immediately with begin of irradiation.
-V0
1)
2)
3)
4)
5)
6)
Interpretation:
Light comes in bundles (photons) with energy E = hf, each photon is absorbed by a single electron.
 # of electrons  # of incident photons
 e– emitted only if photon energy is larger than e– separation energy (“work function”): hf > w0
 Kinetic energy of electron: Ekin, max = h f – w0
stopping potential: eV0 = Ekin, max = h f – w0 ; threshold frequency (Ekin = 0) : f 0 = w0/h
f
Wilhelm Röntgen – X-rays
Roentgen’s original tube
Vacuum tube
Cathode
Anode
cathode rays
–
+
Very first “medical” x-ray exposure:
Berta Roentgen’s hand, December 22, 1895
http://www.deutsches-museum.de/sammlungen/ausgewaehlte-objekte/meisterwerke-ii/roentgen/
Bragg reflection of x-rays
Wave front
q
d
d sin q
Crystal lattice
Bragg condition:
2d sin q = nl
Crystal
x-ray
www.unl.edu/ncmn/facilities/images/Lauebkg_sm.gif
Bragg reflection of x-rays
Polycrystalline
powder
Single crystal
Compton Scattering
Ee, pe
Ei, pi
j
q
Ef, pf
Conservation of energy
Ei + mec2 = Ef + Ee
Conservation of momentum
x: pi
= pf cos q + pe cos j
y: 0
= pf sin q + pe sin j
Ee2 = pe2c2 + me2c4 ; Ei,f = pi,f c
Change in wavelength:
Dl = lC (1-cosq)
with lC = h/mec = 2.43×10-12 m
Electromagnetic Spectrum
Temperature [K]
1014
1012
1010
1010
108
Energy [eV]
108
106
γ-rays
Frequency [Hz]
1024 1022
10-16 10-14
Wavelength [m]
106
104
x-rays
1020
10-12
1018
10-10
104
102
102
100
ultraviolet
1016
10-8
100
10-2
10-6
10-4
10-4
10-6
microwave
infrared
1014
10-2
1012
10-4
10-8
10-10
radio
1010
10-2
10-6
108
100
106
102
104
104
Visible
Wavelength [nm] 400
450
500
550
600
650
700
750
Light emission Spectra
Radiation of gases (e.g. H) – discrete spectrum
Source: http://mo-www.harvard.edu/Java/MiniSpectroscopy.html
Source: http://library.tedankara.k12.tr
Thermal radiation – continuous spectrum
X-ray emission
Bremsstrahlung + characteristic emission
Source: http://www.uni-koeln.de/math-nat-fak/geomin/images/ausstattung/xerzeug.gif
Cross section and Interaction Probability
Target, rt
Projectile, rp
Cross section:
p(rp+rt)²
Number of interactions N:
N = nsfDt
n: number of targets per area
s: (total) cross section
[ ns: fraction of total area covered with “disks”]
f: flux of projectiles (# of projectiles/time)
[ fDt: total number of projectiles]
Interaction probability per projectile P: P = ns
Cross section and Interaction Probability
Cross section for the
interaction of photons
with C atoms
(1 barn = 10-28 m²)
http://xdb.lbl.gov/Section3/Sec_3-1.html
Photo effect
Pair production
(momentum transfer
to nucleus)
Thomson
scattering
Compton
scattering
Pair production
(momentum transfer
to electron)
Matter and Radiation
Energy from matter to radiation: emission
- Continuous: thermal radiation, bremsstrahlung
- Discrete: atomic spectra, characteristic x-rays
- Radioactive decay (gamma radiation, but also other radiation)
Energy from radiation to matter: absorption, scattering
- Photoelectric effect
- Compton scattering
- Pair production
Cross section(s)
Probability for interaction
(Number of interactions N = nsfDt, n: targets per area, f : flux of projectiles)
Attenuation
Beam of photons propagating through material
Intensity at position x: I(x)
Intensity at x+dx: I(x) – probability that something happens in dx
 I(x+dx) = I(x) – I(x)sn = I(x) – I(x)srdx (r : atoms per volume)
 dI/dx = (I(x+dx) – I(x))/dx = – srI(x)
 I(x) = I0 exp( – sr x)