PHYSICS 2D
PROF. HIRSCH
QUIZ 3
Formulas:
Time dilation; Length contraction : Δt = γΔt'≡ γ Δt p ;
WINTER QUARTER 2009
FEBRUARY 6, 2009
L = Lp /γ
; c = 3 ×10 8 m /s
1
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Lorentz transformation : x'= γ (x − vt) ; y' = y ; z' = z ; t'= γ (t − vx /c 2 ) ; inverse : v → -v
Spacetime interval : (Δs) 2 = (cΔt) 2 - [Δx 2 + Δy 2 + Δz 2 ]
uy
ux − v
Velocity transformation : ux '=
; uy '=
; inverse : v → -v
2
1− ux v /c
γ (1− ux v /c 2 )
Relativistic Doppler shift : f obs = f source 1+ v /c / 1− v /c (approaching)
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Momentum, energy (total, kinetic, rest) : p = γ m u; E = γ mc 2 ; K = (γ −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
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→
→
2
; electron volt : 1eV = 1.6 ×10 -19 J
€ Atomic mass unit : 1 u = 931.5 MeV /c
Stefan's law : etot = σT 4 , 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 n / kB T
Planck : E n = nhf ; probability P(E n ) ∝ e
; E ( λ,T) = ∑ E n P(E n ) / ∑ P(E n )
n
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r
Force in electric and magnetic fields (Lorentz force) : F = qE + qv × B ;
Drag force : D = 6πaηv
C
Rutherford scattering : Δn = 4
sin (φ /2)
1
1
1
1
Hydrogen spectrum :
= R( 2 − 2 )
;
R = 1.097 ×10 7 m−1 =
λmn
m
n
911.3A
2
2
2
2
ke Z
Z E
ke
mv
ke 2 Z
ke 2 Z
Bohr atom : E n = −
= − 2 0 ; E0 =
= 13.6eV ; K = e =
; U =−
2rn
n
2a0
2
2r
r
a0
Z
h2
= 0.529A ; L = me vr = nh angular momentum
me ke 2
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hf = E i − E f ; rn = r0 n 2 ; r0 =
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Justify all your answers to all problems
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n
8π
hc / λ
Planck's law : u( λ,T) = N( λ) × E ( λ,T) = 4 × hc / λkB T
λ
e
−1
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
h
h
Compton scattering : λ'- λ =
(1− cos θ ) ;
= 0.0243A
mec
mec
kq q
kq q
Electrostatics : F = 12 2 (force) ; U = 1 2 (potential energy)
r
r
r
r
r
; a0 =
Problem 1 (10 points)
Radiation with a continuous range of wavelengths in the range 110 A to 150 A are incident
on a gas of hydrogen-like ions. Only two absorption lines are seen.
(a) Find the Z of this ion and the wavelengths of the absorption lines, in A.
(b) In this experiment, radiation is also emitted by this gas. How many emission lines are
seen, and what are their wavelengths, in A?
(c ) What is the ionization energy of this ion, in eV?
PHYSICS 2D
PROF. HIRSCH
QUIZ 3
WINTER QUARTER 2009
FEBRUARY 6, 2009
Problem 2 (10 points)
For an electron in the n=2 level of He+:
(a) Give the radius of the orbit, in A.
(b) Give the potential and kinetic energy of this electron, in eV.
(c ) Give the speed of the electron, expressed as v/c.
Problem 3 ( 10 points)
For an electron in a hydrogen atom:
(a) Give the radii of the orbits in the n=9 and the n=10 levels, in A.
(b) Find the classical frequencies of the circular motion of the electron in the n=9 and in the
n=10 orbits, f9 and f1 0, and give the results expressed as hf9 ,, hf1 0 in units eV. (classical
frequency is number of revolutions per second).
(c ) Find the energy (in eV) of the photon emitted when the electron makes a transition from
the n=10 to the n=9 level according to Bohr's theory, and explain the relation between this
result and the results in (b).
Justify all your answers to all problems