7/29/2019 PC1144 Summary (Chapter 37-39)
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1. Special Relativity
(a) Einsteins First Postulate: The Laws of Physicsare the same
in every inertial frame of reference.
(b) Einsteins Second Postulate: The speed of lightin a vacuum c
is the same in all inertial framesof reference and is independent
of the motion ofthe source.
(c) Lorentz Factor: =1
1 v2/c2(d) Time Dilation: t = t0 where t0 is the
proper time.
(e) Length Contraction: l = 1l0 where l0 isthe proper time.
(f) Doppler Effect: f = f0
c + u
c u if the source ismoving towards the observer at the speed of
u,
and f = f0
c uc + u
if the source is moving away
from the observer.(g) Transverse Doppler Effect: f = 1f0 when
the
source passes an observer at closest approachwith speed u.
(h) Lorentz Transformation:
x = (x ut)y = y
z = z
t = (t ux/c2)
(i) Lorentz Velocity Transformation:
vx =vx u
1 uvx/c2(j) Relativistic Mass: m = m0
(k) Relativistic Momentum: p = mv
(l) Newtons Second Law:F
m= a+v3
v ac2
, Fy =
may, Fz = maz, Fx = 3max
(m) Total Energy: E= mc2
(n) Kinetic Energy: K= ( 1)mc2
(o) Rest Energy: Erest = mc2
(p) E2 = (mc2)2 + (pc)2
2. Photons
(a) Energy of a photon: E= hf =hc
(b) Photoelectric Effect: eV0 = hf where e is theelectron
charge, V0 is the stopping potential,
is the work function of a material.
(c) X-ray Production: eVAC hfmax =hc
minwhe
VAC is the voltage difference between cathodand anode
(d) Compton Scattering: = hmec
(1 cos )
(e) Heisenbergs Uncertainty Principle: xpxh
4, ypy
h
4, zpz
h
4, tE
h
4
3. Electrons and Atoms
(a) de Broglies Wavelength: =h
p=
h
mv
(b) Electron Diffraction: d sin = m =mh
2meeVwhere d is the spacing of the diffraction gratinm is the
order of the fringe, Vab is the accelertion voltage.
(c) Bohrs Postulate: Ln = mevnrn =nh
2
(d) Orbital speed of electrons in a hydrogen atomvn =
1
0
e2
2nh
(e) Orbital radius of electrons in a hydrogen atom
rn = 0n2h2
mee2
(f) Energy of an electron in a hydrogen atom:
En = 1
20
mee4
8n2h2= hc
n2R where R = 1.097
107 is the Rydbergs constant.
(g) Transition Wavelength:1
= R
1
n2
L 1
n2
L
(h) Reduced Mass: mr =m1m2
m1 + m2(i) Maxwell-Boltzmann Distribution:
ni = AeEi/kT where ni is the number of atom
with energy Ei and k is the Boltzmann consta(k = 1.381 1023 K J1
= 8.617 105 eK1)
(j) Stefan-Boltzmann Law for blackbody radiatioI = T4 where =
5.67 108 W m2 K4.
(k) Wien Displacement Law: mT = 2.90
103
K
(l) Plancks Radiation Law: I() 2hc2
5(ehc/kT 1)
