Wolfram Alpha:
Search by keyword:
Astronomy
Chemistry
Classical Physics
Climate Change
Cosmology
Finance and Accounting
General Relativity
Lagrangian and Hamiltonian Mechanics
Macroeconomics
Mathematics
Microeconomics
Particle Physics
Probability and Statistics
Programming and Computer Science
Quantum Field Theory
Quantum Mechanics
Semiconductor Reliability
Solid State Electronics
Special Relativity
Statistical Mechanics
String Theory
Superconductivity
Supersymmetry (SUSY) and Grand Unified Theory (GUT)
test
The Standard Model
Topology
Units, Constants and Useful Formulas
Compton Effect
--------------
Photons scattered from electrons had longer wavelength than those incident
upon the target. Gave clear and independent evidence of particle-like behavior
in support of the photoelectric effect.
recoiled electron pe= √(E2 - (mec2)2)/c
^
/
/
/
photon ------->o.....
pi = h/λi \θ
\
\
v
scattered photon
pf = h/λf
Conservation f energy:
hνi + mec2 = hνf + √(pe2c2 + me2c4)
Conservation of momentum:
_ _ _
pi = pe + pf
_ _ _ _
pe2 = (pi - pf).(pi - pf)
= pi2 + pf2 - 2pipfcosθ
multiply by c2 and substitute E = pc = hν
(pec)2 = (hνi)2 + (hνf)2 - 2h2νiνfcosθ
square energy conservation expression to get
(pec)2 = (hνi)2 + (hνf)2 - 2h2νiνf + 2mec2(hνi - hνf)
-2h2νiνfcosθ = -2h2νiνf + 2mec2(hνi - hνf)
which leads to
λf - λi = (h/mec)(1 - cosθ)
Compton Wavelength
--------------------
The Compton wavelength of a particle is equivalent to the wavelength
of a photon whose energy is the same as the rest-mass energy of the
particle.
The Compton wavelength, λ, is derived as follows:
E = hf = hc/λ = mc2
∴ λ = h/mc