PHYSICS 2D
PROF. HIRSCH
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QUIZ 3
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
γ (1− ux v /c 2 )
1− ux v /c
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
Compton scattering : λ'- λ =
h
(1 − cos θ ) ;
mec
h
= 0.0243A
mec
kq q
kq
kq q
Coulomb force : F = 12 2 ; Coulomb energy : U = 1 2 ; Coulomb potential : V =
r
r
rr
r
r r
Force in electric and magnetic fields (Lorentz force): F = qE + qv × B
1
Z2
ke 2 = 14.4 eV A
Rutherford scattering : Δn = C 2
4
Kα 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
Z
ke Z
ke
me (ke )
mev 2
ke 2 Z
Bohr atom : E n = −
= −E 0 2 ; E 0 =
=
= 13.6eV ; K =
; U =−
n
2a0
2
2rn
2h 2
r
hf = E i − E f ; rn = r0 n 2 ; r0 =
a0
Z
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WINTER QUARTER 2016
FEBRUARY 12, 2016
de Broglie : λ =
h
E
;f =
p
h
; a0 =
h2
= 0.529A ; L = me vr = nh angular momentum
me ke 2
; ω = 2πf ; k =
2π
;
λ
Wave packets : y(x,t) = ∑ a j cos(k j x − ω j t), or y(x,t) =
E = hω ; p = hk ;
∫ dk a(k) e
i(kx -ω (k )t )
E=
p2
2m
; ΔkΔx ~ 1 ; ΔωΔt ~ 1
j
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group and phase velocity : v g =
dω
ω
; vp =
;
dk
k
Heisenberg : ΔxΔp ~ h ; ΔtΔE ~ h
PHYSICS 2D
PROF. HIRSCH
QUIZ 3
WINTER QUARTER 2016
FEBRUARY 12, 2016
Problem 1
An electron in hydrogen is initially in a Bohr orbit of radius 121a0 (a0=0.529A). What is
the longest wavelength photon it can emit?
A: 850,000A; B: 525,000A; C: 175,000A; D: 35,000A; E: not sure
Problem 2
The electron in the ground state of a hydrogen atom is moving at a speed twice as fast as
the electron in the state n of the He+ ion, where
A: n=2; B; n=3; C: n=4; D: n=8; E: not sure
(E always counts 0.31 points)
Problem 3
Radiation of wavelengths in the range 1000A to 1050A is incident on a gas of hydrogen
atoms where the electrons are initially in the ground state. Photons are absorbed and
subsequently emitted. The longest wavelength photon emitted has wavelength
approximately
A: 18,746A; B: 4340A; C: 1215A; D: 6560A; E: not sure
Problem 4
For the case of problem 3, the second longest wavelength photon emitted has wavelength
A: 1215A; B: 1025A; C: 2075A; D: 4340A; E: not sure
Problem 5
What is approximately the de Broglie wavelength for an electron in the n=3 orbit of the
hydrogen atom? (A=Angstrom)
A: 6A ; B: 8A; C: 10A; D: 12A; E: not sure
Problem 6
An electron has de Broglie wavelength 0.6135A. Its kinetic energy is approximately
A: 100eV; B: 200eV; C: 300eV; D: 400eV; E: not sure
Problem 7
A wavepacket is formed by superposition of two waves with wavenumbers k1=1A-1,
k2=1.1A-1 that have frequencies w1=2s-1, w2=2.4s-1. The ratio of group velocity to phase
velocity is approximately
A: 2; B: 1 ; C: 1/2 ; D: impossible to say; E: not sure
Problem 8
An electron in a box of size L has kinetic energy 1000eV. L cannot be smaller than: (give
the largest possible answer)
A: 1A; B: 0.1A; C: 0.01A; D: 0,001A; E: not sure