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GRE Physics

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.

1. Stark Effect
I = I_cm + (1/2)m d^2
When you apply a uniform electric field - it induces a dipole moment and interacts with it - and that effect depends on |mj |. So if j is an integer - splits (asymmetrically) into j+1 levels - and if j is a half integer - splits (asymmetrically) into
.5 LI²
? = 5/3

2. Boltzmann / Canonical distribution
I = I_cm + (1/2)m d^2
I = Im (sinc²(a)) ; a = pai sin(?) / ?
E = Z²*E1
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

3. Current in resistor in RC circuit
dU = 0 ? dS = ?dW/T
I = V/R exp(-t/RC)
4H + 2e- ? He +2? + 6?
B = µ0 I n

4. EM: Maxwell'S equations
T = I?²/2
J = E s - s = Conductivity - E = Electric field
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)

5. Stefan-Boltzmann law for blackbodies (power per area and T)
P/A = s T^4
Asin(?) = m?
I = I_0 Cos[?]^2
When you apply a uniform electric field - it induces a dipole moment and interacts with it - and that effect depends on |mj |. So if j is an integer - splits (asymmetrically) into j+1 levels - and if j is a half integer - splits (asymmetrically) into

6. Doppler Shift for light
E = <?| H |?>
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
? = ?0 root((1-v/c)/(1+v/c))
I = I_cm + (1/2)m d^2

7. Bragg'S Law of Reflection
M? = 2dsin(?)
? = h/mv
<?|O|?>
C_eq = ?C_i

8. EM: Reactance of Capacitor
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
X_C = 1/(i?C)
Ct²-x²-y²-z²
P² ~ R³

9. Wein'S displacement law for blackbodies (? and T)
4H + 2e- ? He +2? + 6?
?_max = b/T
S = k ln[O] ; dS = dQ/T
F = qv×B

10. Polarizers - intensity when crossed at ?
V = -L di/dt
F = s * T4
I = I_0 Cos[?]^2
S_mean = s/Sqrt[N]

11. Selection Rules
V = V0 + V0 a ?T
I ' = I cos²(?)
V(r) + L²2/2mr²
?s = 0 - ?l = ±1

12. Atom: Bohr Formula
E = Z²*E1
E²-p²c²
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
N²/Z (m_elec/m_red)

13. EM: Reactance of Inductor
X_L = i?L
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
E = s/e_0
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

14. Thermo: Adiabatic Work vs Isothermal Work
W_A < W_I
Faraday/Lenz: current inducted opposes the changing field
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
Z_c = -i/(?C) ; Z_L = i ? L

15. Lagrangian and Lagrange'S equation
?? = h/mc * (1-cos(?))
L = T - V dL/dq = d/dt dL/dqdot
? = 1.22? / d
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

16. Magnetic Field For Current in Long Wire
µ0 I / 2pR
L = L_0 Sqrt[1-v^2/c^2]
<T> = -<V>/2
Cv = dE/dT = 3R

17. Rotation matrix (2x2)
Cos[?] Sin[?] -Sin[?] Cos[?]
Isentropic
Dp/dt = L / (t ?V)
T^2 = k R^3 - k=constant

18. Quant: [L_x -L_y] = ?
T^2 = k R^3 - k=constant
P² ~ R³
ih_barL_z
I ' = I cos²(?)

19. Thermo: Monatomic gas ?=?
F = µ0 q v I / 2pr
U - ts = -tlog(Z)
? = 5/3
dQ = dW +dU

20. Thin Film Theory: Constructive / Destructive Interference
F = -2*m(? x r)
µ=s^2
In Zeeman effect - the contribution of electron spin to total angular momentum means that it isn'T always three lines and they are not always equally spaced.
Const: 2t = (n +.5)? Destructive 2t = n?

21. Solid: Resistivity of Semi-Conductor
I = -(c ?t)^2 + d^2
?~1/T
µ = m_e/2
F = R/2

22. Doppler Shift in Frequency
F = f* (c+v_r)/(c+v_s)
? = 1.22?/D
T^2 = k R^3 - k=constant
U - ts = -tlog(Z)

23. EM: SHO (Hooke)
S = (hbar/2) s ;with S = S_x xhat + S_y yhat + S_z zhat -s = s_x xhat + s_y yhat + s_z zhat
I = Im (sinc²(a)) ; a = pai sin(?) / ?
?_max = b/T
ma + kx = 0

24. Mech: Force of Friction
F_f = µ*F_N
F = -2*m(? x r)
Infinitely close to equilibrium at all times
DS = 0 - dQ = 0 - P V^? = constant

25. Source Free RL Circuit
dU = 0 ? dS = ?dW/T
ds² = (c*dt)² - ?(x_i)²
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
NC?T

26. QM: de Broglie Wavelength
?= h/v(2mE)
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
? = 5/3
ds² = (c*dt)² - ?(x_i)²

27. Work done on a gas
DW = P dV
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
Q = CVexp(-t/RC)

28. Internal Energy of an Ideal Gas
Dp/dt = L / (t ?V)
U - ts = -tlog(Z)
(3/2) n R ?t
? = 1.22?/D

29. EM: Bremsstrahlung (translation)
Braking Radiation
<?|O|?>
DS = 0 - dQ = 0 - P V^? = constant
1/ne - where n is charge carrier density

30. EM: Method of Images
(° of Freedom)kT/2
W_A < W_I
.5 LI²
Opposing charge induced upon conductor

31. Helmholtz Free Energy
Exp(N(µ-e)/t)
J = E s - s = Conductivity - E = Electric field
W' = (w-v)/(1-w v/c^2) ; observer in S sees an object moving at velocity w; another frame S' moves at v wrt S.
U - ts = -tlog(Z)

32. Hall Coefficient
H = H_0 + ?H
1/ne - where n is charge carrier density
S = (hbar/2) s ;with S = S_x xhat + S_y yhat + S_z zhat -s = s_x xhat + s_y yhat + s_z zhat
Sin(?) = ?/d

33. Atom: Orbital Config
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
F = mv²/r
NC?T
µ0 I1I2 / (2pd)

34. Rocket Thrust
I = V/R exp(-t/RC)
u dm/dt
F = I L X B
S_mean = s/Sqrt[N]

35. Planck Radiation Law
Cos[?] Sin[?] -Sin[?] Cos[?]
S = k ln[O] ; dS = dQ/T
Z²/n² (m_red/m_elec)
Hbar*?³/(p²c³exp(hbar?/t)-1)

36. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
F = µ0 q v I / 2pr
Faraday/Lenz: current inducted opposes the changing field
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.

37. E field of a capacitor (d->0)
PdV +dU
qvb = mv²/R
E = s/e_0
? = 1.22?/D

38. Rayleigh criterion
? = 1.22? / d
µ0 I1I2 / (2pd)
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
Exp(N(µ-e)/t)

39. Angular momentum operators L^2 and L_z
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
S = k ln[O] ; dS = dQ/T
J = E s - s = Conductivity - E = Electric field
I = I_cm + (1/2)m d^2

40. Complex impedance (expressions for capacitor and inductor)
C_eq = ?C_i
Z_c = -i/(?C) ; Z_L = i ? L
dU = 0 ? dS = ?dW/T
?max = 2.898 x 10 -³ / T

41. Work in a capacitor
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
1/2 CV²
.5 CV²
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.

42. Double Slit: Interference Minimum - Diffraction Minimum
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
.5 LI²
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas

43. Anomalous Zeeman Effect

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44. Astro: p-p Chain
Sin(?) = ?/d
4H + 2e- ? He +2? + 6?
I = I_cm + md²
?s = 0 - ?l = ±1

45. Expectation value of the energy of state |?>
E = <?| H |?>
U - ts = -tlog(Z)
J/(ne) n: atom density
v(mean)

46. Selection rules for atomic transitions
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
J/(ne) n: atom density
N²/Z (m_elec/m_red)
? exp(-e/t)

47. Rocket Equation
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
dU = 0 ? dS = ?dW/T
Dv = -udm/m - v = v0 + u ln(m0/m)
I = I_cm + (1/2)m d^2

48. Atom: Hydrogen Wave Function Type
Exponentially decreasing radial function
Int ( A . dr) = Int ( del x A) dSurface
.5 CV²
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

49. Relativistic Energy
Infinitely close to equilibrium at all times
L = L_0 Sqrt[1-v^2/c^2]
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
?mc²

50. Bohr Model: Radii
N²/Z (m_elec/m_red)
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
When you apply a uniform electric field - it induces a dipole moment and interacts with it - and that effect depends on |mj |. So if j is an integer - splits (asymmetrically) into j+1 levels - and if j is a half integer - splits (asymmetrically) into