PHYSICS 2D
PROF. HIRSCH
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QUIZ 2
WINTER QUARTER 2016
JANUARY 29, 2016
Formulas:
Time dilation; Length contraction : Δt = γΔt'≡ γ Δt p ;
L = Lp /γ
; c = 3 ×10 8 m /s
Lorentz transformation : x'= γ (x − vt) ; y' = y ; z' = z ; t'= γ (t − vx /c 2 ) ; inverse : v → -v
uy
ux − v
Velocity transformation : ux '=
; uy '=
; inverse : v → -v
2
1− ux v /c
γ (1− ux v /c 2 )
Spacetime interval : (Δs) 2 = (cΔt) 2 - [Δx 2 + Δy 2 + Δz 2 ]
Relativistic Doppler shift : f obs = f source 1+ v /c / 1− v /c
r
r
Momentum : p = γ mu ; Energy : E = γ mc 2 ; Kinetic energy : K = (γ −1)mc 2
Rest energy : E 0 = mc 2
Electron : me = 0.511 MeV /c 2
;
E=
p 2c 2 + m 2c 4
Proton : mp = 938.26 MeV /c 2
Neutron : mn = 939.55 MeV /c 2
Atomic mass unit : 1 u = 931.5 MeV /c 2
; electron volt : 1eV = 1.6 ×10 -19 J
4
Stefan's law : etot = σT , etot = power/unit area ; σ = 5.67 ×10−8 W /m 2K 4
∞
hc
etot = cU /4 , U = energy density = ∫ u( λ,T)dλ ;
Wien's law : λm T =
4.96kB
0
-E/(kB T )
Boltzmann distribution : P(E) = Ce
8π
hc / λ
8πf 2
Planck's law : uλ ( λ,T) = N λ ( λ) × E ( λ,T) = 4 × hc / λkB T
;
N( f ) = 3
λ
e
−1
c
Photons : E = hf = pc ; f = c / λ ; hc = 12,400 eV A ; k B = (1/11,600)eV /K
Photoelectric effect : eVs = K max = hf − φ , φ ≡ work function; Bragg equation : nλ = 2d sin ϑ
h
= 0.0243A
mec
kq q
kq q
kq
Coulomb force : F = 12 2 ; Coulomb energy : U = 1 2 ; Coulomb potential : V =
r
rr
r
r
r r
Force in electric and magnetic fields (Lorentz force) : F = qE + qv × B
Z2
1
Rutherford scattering : Δn = C 2
ke 2 = 14.4 eV A
4
Kα sin (φ /2)
Problem 1
A black body is initially at temperature T=1000K, then its temperature is increased to
2000K. In this process, the power emitted by this body for wavelengths in the range
5000A to 5001A increases by a factor of approximately:
A: 2; B: 16; C: 2,000; D: 2,000,000; E: not sure (E always counts 0.21 points)
Compton scattering : λ'- λ =
h
(1 − cos θ ) ;
mec
Problem 2
A black ball emits the same total power as another black ball with twice its radius. If the
small ball emits maximum power at wavelength 3000A, the large ball emits maximum
power at wavelength approximately:
A: 4200A; B: 5000A; C: 6400A; D: 2600A; E: not sure
Problem 3
A light source emits 3W of power of wavelength 2000A. How many photons does it emit
per second approximately?
A: 6x1017; B: 3x1018 ; C: 2x1019 ; D:1020; E: not sure
PHYSICS 2D
PROF. HIRSCH
QUIZ 2
WINTER QUARTER 2016
JANUARY 29, 2016
Problem 4
A light source of wavelength 5000A shining on a metal surface produces no
photoelectrons. However if this light source is moving and approaching the metal at
speed 1/2 of the speed of light, photoelectrons of maximum kinetic energy 1eV are
detected. What is approximately the work function of this metal?
A: 1.5eV; B; 3.3eV C: 2,8eV; D: 3.6eV; E: not sure
Problem 5
In a Compton scattering experiment with a monochromatic X-ray source, photons
scattered at angle 30o relative to the direction of incidence have wavelength 1A. What is
approximately the kinetic energy of the scattered electron?
A: 200eV; B: 233eV; C: 266eV; D: 300eV; E: not sure
Problem 6
The charge to mass ratio for an electron is 1.76x1011 C/kg.
In a Thomson vacuum tube the applied electric field of 100 V/cm between parallel plates
of length ℓ =4cm deflects electrons as they enter the space between the plates traveling
in direction parallel to the plates at a speed 2x107m/s. The angle at which the electrons
are deflected relative to the incident direction when they emerge from the region between
the plates is approximately, in radians:
A: 0.170; B: 0.172; C: 0.174; D: 0.176; E: not sure
Problem 7
In a Rutherford scattering experiment with a metal foil with atoms of atomic number
Z=20 and using 8MeV α particles the Rutherford law given in the list of formulas is
found to be satisfied for all angles. What can you say about the radius of this nucleus, R?
(1fm=10-5A)
A: R<7.2fm; B: R>7.2fm; C: R>3.6fm; D: R<3.6fm; E: not sure
Problem 8
For the Rutherford scattering experiment of problem 7 suppose the energy of the
α particles is now increased to 10MeV, and it is found that for every 1600 particles
scattered at 60o angle there are 400 particles scattered at 90o angle. How many particles
are scattered at 180o angle for every 1600 particles scattered at 60o angle?
A: 100; B: 100 or more than 100; C: 100 or less than 100; D: impossible to say; E: not
sure