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GRE Physics

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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. Wein'S displacement law for blackbodies (? and T)
?_max = b/T
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
Z_c = -i/(?C) ; Z_L = i ? L
Dv = -udm/m - v = v0 + u ln(m0/m)

2. Kepler'S third law (T and R)
1/vLC
Opposing charge induced upon conductor
T^2 = k R^3 - k=constant
E²-p²c²

3. Rocket Equation
? = 5/3
Opposing charge induced upon conductor
Dv = -udm/m - v = v0 + u ln(m0/m)
F = R/2

4. Helmholtz Free Energy
F = f* (c+v_r)/(c+v_s)
? = 1.22? / d
U - ts = -tlog(Z)
?~T

5. Triplet/singlet states: symmetry and net spin
PdV +dU
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
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
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

6. Rocket Thrust
DW/dq
? (t-vx/c²)
u dm/dt
Z = ?g_i*exp(-E/kT)

7. Stark Effect
ma + kx = 0
?mc²
ds² = (c*dt)² - ?(x_i)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

8. Compton Scattering
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
C_eq = (? 1/C_i)^-1
4H + 2e- ? He +2? + 6?
?? = h/mc * (1-cos(?))

9. Law of Mass Action
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
?mv
1/2 CV²
F = qv×B

10. Current in resistor in RC circuit
I = V/R exp(-t/RC)
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

11. Atom: Orbital Config
T = I?²/2
µ0 I / 2pR
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
Dv = -udm/m - v = v0 + u ln(m0/m)

12. Work in a capacitor
I = I_0 Cos[?]^2
?= h/v(2mE)
1/2 CV²
H = H_0 + ?H

13. Lab: Precision of Measurements
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
? (t-vx/c²)
Z = ?g_i*exp(-E/kT)
Measurements close to mean

14. Doppler shift for light
L = mr²d?/dt
E = Z²*E1
F_f = µ*F_N
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

15. Work (P - V)
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
C_eq = ?C_i
? = 1.22? / d
P1V1 - P2V2 / (? - 1)

16. RLC resonance condition
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
J = E s - s = Conductivity - E = Electric field

17. Bohr Model: Energy
F = I L X B
Z²/n² (m_red/m_elec)
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
F = R/2

18. Wein'S Displacement Law
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
?max = 2.898 x 10 -³ / T
qvb = mv²/R
? = h/p

19. Quant: Orthogonality of States
L = L_0 Sqrt[1-v^2/c^2]
<?1|?2> = 0 ? Orthogonal
I = V/R exp(-t/RC)
J = ? Fdt

20. Solid: Resistivity of Semi-Conductor
? (t-vx/c²)
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
?~1/T
? exp(-e/t)

21. Selection Rules
DW = P dV
qvb = mv²/R
?s = 0 - ?l = ±1
F = R/2

22. Stefan-Boltzmann law for blackbodies (power per area and T)
P/A = s T^4
DW = P dV
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
Opposing charge induced upon conductor

23. Parallel axis theorem
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
µ = Current * Area T = µ x B
I = I_cm + (1/2)m d^2
Infinitely close to equilibrium at all times

24. Mean electron drift speed
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
Ct²-x²-y²-z²
I ' = I cos²(?)
J/(ne) n: atom density

25. Thermo: Adiabatic Work vs Isothermal Work
L = L_0 Sqrt[1-v^2/c^2]
W_A < W_I
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
X_C = 1/(i?C)

26. SR: Spacetime Interval
?mv
P +1/2 ? v² + ?gh = Constant
ds² = (c*dt)² - ?(x_i)²
P1V1 - P2V2 / (? - 1)

27. 3 Laws of Thermo
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
dU = 0 ? dS = ?dW/T
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

28. Bernoulli Equation
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
P +1/2 ? v² + ?gh = Constant
M? = 2dsin(?)
µ0 I1I2 / (2pd)

29. Mech: Force of Friction
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
F = µ0 q v I / 2pr
F_f = µ*F_N
DS = 0 - dQ = 0 - P V^? = constant

30. Internal Energy of an Ideal Gas
?s = 0 - ?l = ±1
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
(3/2) n R ?t
F = I L X B

31. Heat added
L = L_0 Sqrt[1-v^2/c^2]
V = V0 + V0 a ?T
NC?T
Sin(?) = ?/d

32. EM: Lorentz Force
F = qv×B
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
P +1/2 ? v² + ?gh = Constant

33. Astro: Kepler'S Third Law
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
?_max = b/T
P² ~ R³
A[B -C] + [A -C]B

34. Bar magnets -- direction of B field lines - earth'S B field
?max = 2.898 x 10 -³ / T
U = t^2 d/dt (logZ)
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
?mv

35. Single Slit Diffraction Intensity
µ=s^2
V = V0 + V0 a ?T
I = Im (sinc²(a)) ; a = pai sin(?) / ?
Z = ?g_i*exp(-E/kT)

36. Complex impedance (expressions for capacitor and inductor)
L = mr²d?/dt
X_L = i?L
L = T - V dL/dq = d/dt dL/dqdot
Z_c = -i/(?C) ; Z_L = i ? L

37. Quant: Eigenvalue of Hermitian Operator
P/A = s T^4
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
ih_barL_z
Always Real

38. Doppler Shift for light
? = 1.22? / d
? = ?0 root((1-v/c)/(1+v/c))
µ=s^2
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

39. Kepler'S Three Laws
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
L = mr²d?/dt
J = E s - s = Conductivity - E = Electric field
Hbar*?³/(p²c³exp(hbar?/t)-1)

40. Mech: Virial Theorem
X_L = X_C or X_total = 0
? = 1.22?/D
<T> = -<V>/2
I = V/R exp(-t/RC)

41. Expectation value of the energy of state |?>
P1V1 - P2V2 / (? - 1)
F = mv²/r
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
E = <?| H |?>

42. Self Inductance
J/(ne) n: atom density
<T> = -<V>/2
V = -L di/dt
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

43. Anomalous Zeeman Effect

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44. Selection rules for atomic transitions
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
E = Z²*E1
Z²/n² (m_red/m_elec)
V = V0 + V0 a ?T

45. Pauli matrices
F_f = µ*F_N
µ = Current * Area T = µ x B
I = I_cm + md²
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

46. De Broigle Wavelength
?= h/v(2mE)
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
? = h/mv
Q = CVexp(-t/RC)

47. Adiabatic means
P1V1 - P2V2 / (? - 1)
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
F = mv²/r
Isentropic

48. Angular momentum - Central Force Motion
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
L = mr²d?/dt
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...

49. Coriolis Force
? = 1.22?/D
F_f = µ*F_N
4H + 2e- ? He +2? + 6?
F = -2*m(? x r)

50. SR: Total Energy of a Particle
Always Real
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
Const: 2t = (n +.5)? Destructive 2t = n?
µ0 I / 2R