Transcript Physics 2DL Lectures - University of California, San Diego

Physics 2DL Lectures
Vivek Sharma
Lecture # 3
Discussion of Experiments
Franck-Hertz Experiment : A prelude
Bohr Atom : Discrete orbit  Emission & Absorption line
classical
Bohr’s
quantization
n2 2
rn 
, n  1 , 2,....
2
mke
n  1  Bohr Radius a0
 ke2  Z 2
En   
 2
 2a0  n
Franck Hertz Experiment: Playing Football !
Inelastic scattering of electrons
Confirms Bohr’s Energy quantization
Electrons ejected from heated cathode
At zero potential are drawn towards
the positive grid G. Those passing thru
Hole in grid can reach plate P and cause
Current in circuit if they have sufficient
Kinetic energy to overcome the retarding
Potential between G and P
Tube contains low pressure gas of stuff!
If incoming electron does not have
enough energy to transfer =E2-E1 then
Elastic scattering, if electron has atleast
KE=  then inelastic scattering and the
electron does not make it to the plate P
 Loss of current
(J) Franck & (G) Hertz Experiment
Current decreases because many
Electrons lose energy due to inelastic
Scattering with the Hg atom in tube
And therefore can not overcome the
Small retarding potential between
GP
The regular spacing of the peaks
Indicates that ONLY a certain quantity
Of energy can be lost to the Hg atoms
=4.9 eV.
This interpretation can be confirmed by
Observation of radiation of photon energy
E=hf=4.9 eV emitted by Hg atom when
V0 > 4.9V
Atomic Spectra
Propagation of Plane Wave in Vacuum : Huygens
Huygen’s theory of Wave propagation allows us to tell
the future location of wave front
•All points on a wave front serve as a point source of
spherical secondary wavelet. After a time t, the new
position of wavefront will be that of a surface tangent to
these secondary wavelets
Coherence of Light: if 2 light waves meet at a point
are to interfere perceptibly, then the phase difference
between them must remain constant with time; that is
waves must be coherent. Degree of coherence of a
source of light is the degree to which light consists of
long, unbroken trains (packets) of Sinusoidal waves
Coherent” Sources : Laser, radiating atom (but they all
have a spread of wavelengths)
Incoherent Source : Light bulb
Wave packet
Diffraction Phenomenon
If a wave encounters a barrier that has an opening of dimensions similar to the
, the part of the wave that passes thru opening will spread out (diffract) into a
region beyond the barrier (spreading of Huygen’s wavelets)
Narrower the slit, larger the diffraction
Diffraction limits geometrical optics (ray tracing)
Young’s Double Slit Interference Experiment
Condition for constructive Interference : Overlapping waves must have same phase
So the path lengths traversed by the two waves must satisfy L= d sin = m  (m=0,1,2,3..)
Destructive Inter. at the screen when 2 waves exactly out of phase d sin = (m+1/2)  (m=0,1,2,..)
With this “simple” idea , Young could measure the average wavelength of the sun (555nm) !
diffraction
diffraction
Michelson’s Interferometer
Interferometer: device to measure lengths or changes in
lengths with great accuracy by means of interference
fringes (big daddy of them all was designed by
Michelson in 1881…first American Nobel prize 1907)
How it works:
• Light from source at P encounters beam splitter
•Beam splitter transmits ½ and reflects ½ of incident
•The 2 waves now head towards M1 and M2 mirrors
•Get reflected entirely and sent back along direction of
incidence and then deflected towards telescope T
•Observer at T sees a pattern of “zebra strip” like fringes
Path length  when 2 waves combine at telescope=2d2 –2d1
anything that changes this path diff  will cause change in phase
diff between two waves at the eye. E.g. If mirror M1 moves by /2
then  changes by  and fringe pattern shifted by 1 (max min)
Single Slit Diffraction
Condition for First Minimum
(a/2) sin = /2
Diffraction Grating: Mechanism & Intensity Distribution
Similar to double-slit except many more slits (ruling)~ 1000
Monochromatic light thru grating forms narrow interference
Fringes(lines) that can be analyzed to determine  of light
If d = grating spacing, show that d Sinm ( condition for maxima)
Width of line =  / (N d Cos )
A Grating Spectrograph
NaCl & X-ray Diffractio : Orientation Important!
n=2dsin 
Bragg Scattering of X-Ray Light
Electron Diffraction : Davisson Germer Expt
Matter Waves
de Broglie Conjecture
h
=
p
Electron Diffraction : Davisson Germer Expt
1 2
p2
mv  K 
 eV
2
2m
2eV
v
;
m
p  mv  m
2eV
m
h
  predict
2meV
Diffraction Pattern in Polycrystalline Al target
Diffraction pattern produced by 600eV electrons incident
on a Al foil target
E.Coli Seen With Electron Microscope