Transcript Review Exam 1

Review Exam 1
Formulas
Time Dilation:
t  t p
Length Contraction:
L 
Relativistic Momentum:
p
Lp

mu
1
u2
c2
Formulas
Relativistic Energy:
Rest Energy:
E0  mc
2
mc
2
Total Energy:
E  K  E0 
1
u2
c2
Useful Formulas for Speed, Energy, and Momentum:
E  hf 
hc

f 
c

E  p c  (mc )
2
2 2
2 2
E  pc,
for
E  mc2
u
pc

c
E
Photoelectric Effect:
 mv2 

eV0  
 hf  
 2 

 max
Compton’s equation:
h
2  1 
(1  cos  )
mec
Plank’s Law:
u ( ) 
2 5
8hc 
hc
e kT
1
R  T
Stefan-Boltzman Radiation Law:
P  AT
Stefan-Boltzman constant:   5.672  10
Wien’s displacement law:
3
max T  cons tan t  2.898 10 m  K
Rayleigh-Jeans Law:
4
u ( )  kTn( )  8kT
4
8
4
W
m2 K 4
m
c  3  10
s
8
h  6.626  1034 J  s  4.135  1015 eV  s
Mass of electron : me  9.1094  1031kg  0.511 MeV
c2
Ch arg e of electron : e  1.6  1019 C
Mass of the proton : m p  1.67  10 27 kg
hc  1.9864  10 25 J  m  1239.8eV  nm
1eV  1.6022  1019 J
• Specific Heat:
• Latent Heat:
Q
c
mT
Q
L
m


Q  mcT
Q   Lm
• Work done by engine: Wengine  Qnet  Qh  Qc
• Thermal Efficiency:
Qh  Qc
Qc
e

 1
Qh
Qh
Qh
Weng
Typical Problems
Two identical twins Speedo and Goslo join a
migration from the Earth to Planet X. It is 20.0 LY
away in a reference frame in which both planets
are in the rest. The twins, of the same age, departs
at the same time on different spacecrafts.
Speedo’s craft travels steadily at 0.950c, and
Goslo’s at 0.750c. Calculate the age difference
between the twins after Goslo’s spacecraft lands
on Planet X. Which twin is the older?
A proton in high-energy accelerator moves
with a speed c/2. Use the work kinetic energy
theorem to find the work required to increase the
speed to (a) 0.750c and (b) 0.995c.
In the constellation Orion we can observe two
bright stars: Betelgeuse appears to glow red, while
Rigel looks blue in color. Which star has a higher
surface temperature? (λred=700nm; λblue=430nm)
Electrons are ejected from a metallic surface with
speed ranging up to 4.60x105 m/s when light with a
wavelength of 625 nm is used. What is the work
function of the metal? What is the cutoff frequency of
this surface?
A 0.110-nm photon collides with a stationary
electron. After the collision, the electron moves
forward and the photon recoils backward. Find the
momentum and the kinetic energy of the electron.
(Compton effect problem)
Find the power per unit area radiated from
the surface of the sun in the wavelength range
600.0 to 605.0 nm
The power output of the Sun is 3.77×1026 W.
How much mass is converted to energy in
the Sun each second?