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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. Mech: Rotational Energy
N²/Z (m_elec/m_red)
Q = CVexp(-t/RC)
T = I?²/2
<?1|?2> = 0 ? Orthogonal

2. Thermo: Average Total Energy
(° of Freedom)kT/2
Braking Radiation
T = I?²/2
A[B -C] + [A -C]B

3. Atom: Hydrogen Wave Function Type
? = 1.22?/D
Exponentially decreasing radial function
P1V1 - P2V2 / (? - 1)
?mc²

4. Mech: Virial Theorem
<T> = -<V>/2
F = -2*m(? x r)
Z = ?g_i*exp(-E/kT)
S_mean = s/Sqrt[N]

5. Center of Mass: Kinetic Energy & Angular Momentum
I ' = I cos²(?)
N²/Z (m_elec/m_red)
X_C = 1/(i?C)
KE = 1/2 * µ (dr/dt)² L = µ r x v

6. EM: Bremsstrahlung (translation)
Braking Radiation
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
F_f = µ*F_N
Cv = dE/dT = 3R

7. Quant: Commutator Relation [AB -C]
C = 4pe0 ab/(a-b) = inner and outer radii
? = 1.22?/D
Isentropic
A[B -C] + [A -C]B

8. De Broglie wavelength
X_L = i?L
qvb = mv²/R
? exp(-e/t)
? = h/p

9. Resistance - length - area - rho
? exp(-e/t)
I = I_cm + md²
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)

10. Atom: Bohr Theory Ionization
W_A < W_I
P +1/2 ? v² + ?gh = Constant
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
E = Z²*E1

11. Effective Potential
? = 5/3
DS = 0 - dQ = 0 - P V^? = constant
V(r) + L²2/2mr²
I = I_0 Cos[?]^2

12. Electromotive Force
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
<?|O|?>
DW/dq
?s = 0 - ?l = ±1

13. Bohr Model: Energy
Measurements close to true value
Z²/n² (m_red/m_elec)
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
?s = 0 - ?l = ±1

14. Quant: Orthogonality of States
P/A = s T^4
DS = 0 - dQ = 0 - P V^? = constant
<?1|?2> = 0 ? Orthogonal
? = h/p

15. Adiabatic processes (dS - dQ - P and V)
U = t^2 d/dt (logZ)
? = 1.22? / d
DS = 0 - dQ = 0 - P V^? = constant
V = -L di/dt

16. Lab: Accuracy of Measurements
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
Measurements close to true value
X_C = 1/(i?C)
? = h/mv

17. Bragg'S Law of Reflection
P² ~ R³
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
M? = 2dsin(?)
1/ne - where n is charge carrier density

18. Helmholtz Free Energy
E = s/e_0
U - ts = -tlog(Z)
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
? exp(-e/t)

19. Perturbations
dQ = dW +dU
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
E = s/e_0
H = H_0 + ?H

20. Lab: Precision of Measurements
Measurements close to mean
F = s * T4
? = h/mv
? = 1.22?/D

21. Spherical Capacitor Equation
?~1/T
1/2 CV²
.5 LI²
C = 4pe0 ab/(a-b) = inner and outer radii

22. How to derive cylcotron frequency
ih_barL_z
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
qvb = mv²/R

23. Kepler'S Three Laws
?? = h/mc * (1-cos(?))
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
Z = ?g_i*exp(-E/kT)

24. Coriolis Force
F = -2*m(? x r)
H = H_0 + ?H
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
DW = P dV

25. Astro: Kepler'S Third Law
J = ? Fdt
? = 1.22?/D
?? = h/mc * (1-cos(?))
P² ~ R³

26. Expectation value of the energy of state |?>
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
E = <?| H |?>
F = µ0 q v I / 2pr
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

27. Energy in terms of partition function
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
Infinitely close to equilibrium at all times
X_L = i?L
U = t^2 d/dt (logZ)

28. Triplet/singlet states: symmetry and net spin
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
X_C = 1/(i?C)
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i

29. Addition of relativistic velocities

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30. Boltzmann / Canonical distribution
Dp/dt = L / (t ?V)
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
Const: 2t = (n +.5)? Destructive 2t = n?
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

31. Compton Scattering
.5 CV²
?? = h/mc * (1-cos(?))
T^2 = k R^3 - k=constant
Measurements close to mean

32. Selection Rules
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
?s = 0 - ?l = ±1
V = -L di/dt
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

33. Lab: Standard Deviation of Poisson
0
? = 1.22? / d
X_L = i?L
v(mean)

34. De Broigle Wavelength
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.
? = h/mv
? = 1.22? / d
Q = CVexp(-t/RC)

35. Anomalous Zeeman Effect

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36. Commutator identities ( [B -A C] - [A -B] )
ma + kx = 0
<?1|?2> = 0 ? Orthogonal
H = H_0 + ?H
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

37. QM: de Broglie Wavelength
Dp/dt = L / (t ?V)
1/vLC
? exp(-e/t)
?= h/v(2mE)

38. Inductance of Solenoid
.5 LI²
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

39. Quant: Expectation Value
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
J = ? Fdt
I = I_0 Cos[?]^2
<?|O|?>

40. Heat added
NC?T
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
µ=s^2
Opposing charge induced upon conductor

41. Relativistic interval (which must remain constant for two events)
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
I = -(c ?t)^2 + d^2
4H + 2e- ? He +2? + 6?
Dp/dt = L / (t ?V)

42. Mech: Parallel Axis Theorem (Moment of Inertia)
I = I_cm + md²
µ = Current * Area T = µ x B
Opposing charge induced upon conductor
Exp(N(µ-e)/t)

43. Bohr Model: Radii
T = I?²/2
N²/Z (m_elec/m_red)
?_max = b/T
L = mr²d?/dt

44. Time Lorentz Transformation
<T> = -<V>/2
F = f* (c+v_r)/(c+v_s)
<?1|?2> = 0 ? Orthogonal
? (t-vx/c²)

45. Rayleigh criterion
4H + 2e- ? He +2? + 6?
E²-p²c²
? = 1.22? / d
v(mean)

46. Parallel axis theorem
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
?~T
I = I_cm + (1/2)m d^2
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h

47. Invariant Energy Quantity
F = s * T4
?max = 2.898 x 10 -³ / T
dU = 0 ? dS = ?dW/T
E²-p²c²

48. RLC resonance condition
V = V0 + V0 a ?T
?mv
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
Measurements close to mean

49. Malus Law

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50. Angular momentum - Central Force Motion
L = mr²d?/dt
V(r) + L²2/2mr²
E = <?| H |?>
F_f = µ*F_N