PHYSICS 2D
PROF. HIRSCH
QUIZ 2
WINTER QUARTER 2009
JANUARY 30, 2009
Formulas:
Time dilation; Length contraction : "t = #"t'$ # "t p ;
; c = 3 %10 8 m /s
L = Lp /#
1
!
!
Lorentz transformation : x'= " (x # vt) ; y' = y ; z' = z ; t'= " (t # vx /c 2 ) ; inverse : v $ -v
Spacetime interval : ("s) 2 = (c"t) 2 - ["x 2 + "y 2 + "z 2 ]
uy
ux " v
Velocity transformation : ux '=
;
u
'=
; inverse : v $ -v
y
1" ux v /c 2
# (1" ux v /c 2 )
Relativistic Doppler shift : f obs = f source 1+ v /c / 1" v /c (approaching)
!
Momentum, energy (total, kinetic, rest) : p = # m u; E = # mc 2 ; K = (# $1)mc 2 ;E 0 = mc 2 ;E = p 2c 2 + m 2c 4
Electron : me = 0.511 MeV /c 2
Proton : mp = 938.26 MeV /c 2
Neutron : mn = 939.55 MeV /c 2
!
!
!
!
!
"
"
2
; electron volt : 1eV = 1.6 "10 -19 J
! Atomic mass unit : 1 u = 931.5 MeV /c
4
Stefan's law : etot = "T , etot = power/unit area ; " = 5.67 #10$8 W /m 2K 4
#
hc
etot = cU /4 , U = energy density = $ u( ",T)d" ;
Wien's law : "m T =
4.96kB
0
#E n / kB T
Planck : E n = nhf ; probability P(E n ) " e
; E ( $,T) = % E n P(E n ) / % P(E n )
n
!
!
!
!
!
!
r
Force in electric and magnetic fields (Lorentz force) : F = qE + qv " B ;
C
sin (# /2)
1
1
1
Hydrogen spectrum :
= R( 2 # 2 )
"mn
m
n
Rutherford scattering : "n =
!
!
n
8$
hc / "
Planck's law : u( ",T) = N( ") # E ( ",T) = 4 # hc / "kB T
"
e
%1
Photons : E = hf = pc ; f = c / " ; hc = 12,400 eV A ; k B = (1/11,600)eV /K
Photoelectric effect : eVs = K max = hf " # , # $ work function
h
h
Compton scattering : "'- " =
(1# cos $ ) ;
= 0.0243A
mec
mec
kq q
kq q
Electrostatics : F = 12 2 (force) ; U = 1 2 (potential energy)
r
r
r
r
r
Drag force : D = 6#a$v
4
;
R = 1.097 $10 7 m#1 =
1
911.3A
!
!
Justify all your answers to all problems
Problem 1 (10 points)
Consider two black bodies at temperatures T1 and T2 respectively. Body #1 looks green
(λ=5200A) and body #2 looks violet (λ=4100 A).
(a) Find their temperatures T1 and T2 in K.
(b) Which of the two bodies emits more power per unit area in the red wavelength range
(λ=6500A)? Justify your answer.
(c) If the two bodies emit the same total power, what can you conclude about the ratio of
their surface areas?
PHYSICS 2D
PROF. HIRSCH
QUIZ 2
WINTER QUARTER 2009
JANUARY 30, 2009
Problem 2 (10 points)
When violet light (λ=4100A) is incident on the surface of a metal, the stopping voltage
for the photocurrent is twice as large as when green light (λ=5200A) is incident on that
metal.
(a) Find the work function of this metal, in eV.
(b) What is the maximum energy of the photoelectrons emitted with violet light and with
green light respectively, in eV?
(c) What is the maximum wavelength of light (in A) that will give rise to photoelectrons
being emitted from the surface of this metal?
Problem 3 ( 10 points)
In a Rutherford experiment with a Cu foil (Z=29), it is found that for every 100 αparticles scattered at angle 120 degrees there are 1,100 α-particles scattered at angle 60
degrees if the energy of the α-particles is 26 MeV, 1,000 particles scattered at 60 degrees
if their energy is 25 MeV, 900 particles scattered at 60 degrees if their energy is 24 MeV
and 800 particles scattered at 60 degrees if their energy is 23 MeV .
(a) One of these four experimental results is wrong, because the experimentalist made a
mistake. Find which one it is, and explain why it's wrong.
(b) Ignoring the result that is wrong, use the other results to find upper and lower bounds
for the radius of the Cu nucleus, in A. Justify your answers.
Justify all your answers to all problems