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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. Clausius-Clapeyron Equation
Dp/dt = L / (t ?V)
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
Exp(N(µ-e)/t)
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i

2. Doppler Shift for light
N²/Z (m_elec/m_red)
I = I_0 Cos[?]^2
NC?T
? = ?0 root((1-v/c)/(1+v/c))

3. Malus Law

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4. Selection rules for atomic transitions
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
?? = h/mc * (1-cos(?))
µ0 I1I2 / (2pd)
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

5. Inductance of Solenoid
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_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.
PdV +dU
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length

6. Virial Theorem
<T> = 1/2 * <dV/dx>
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
? exp(-e/t)
F = µ0 q v I / 2pr

7. Mech: Centripetal Force
Dp/dt = L / (t ?V)
ih_barL_z
L = T - V dL/dq = d/dt dL/dqdot
F = mv²/r

8. EM: Lorentz Force
N d flux / dt
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
Faraday/Lenz: current inducted opposes the changing field
F = qv×B

9. Thermo: Monatomic gas ?=?
E = <?| H |?>
? (t-vx/c²)
? = 5/3
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

10. Quant: Eigenvalue of Hermitian Operator
Always Real
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
Exponentially decreasing radial function
E = <?| H |?>

11. Astro: p-p Chain
F = qv×B
E = <?| H |?>
4H + 2e- ? He +2? + 6?
.5 CV²

12. Quant: [L_x -L_y] = ?
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
I = Im (sinc²(a)) ; a = pai sin(?) / ?
µ = m_e/2
ih_barL_z

13. Lab: Accuracy of Measurements
Measurements close to true value
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
? = 1.22?/D
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

14. Resonance frequency of LC circuit
? exp(-e/t)
1/vLC
? = ?0 root((1-v/c)/(1+v/c))
F = s * T4

15. Rocket Equation
? = 1.22?/D
I = Im (sinc²(a)) ; a = pai sin(?) / ?
NC?T
Dv = -udm/m - v = v0 + u ln(m0/m)

16. Spherical Capacitor Equation
I ' = I cos²(?)
Isentropic
C = 4pe0 ab/(a-b) = inner and outer radii
?max = 2.898 x 10 -³ / T

17. Invariant Energy Quantity
E²-p²c²
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
V = V0 + V0 a ?T
X_L = X_C or X_total = 0

18. Kepler'S third law (T and R)
J/(ne) n: atom density
T^2 = k R^3 - k=constant
F = I L X B
µ0 I1I2 / (2pd)

19. Atom: Positronium Reduced Mass
u dm/dt
<?1|?2> = 0 ? Orthogonal
<T> = -<V>/2
µ = m_e/2

20. Atom: Bohr Theory Ionization
?max = 2.898 x 10 -³ / T
µ0 I / 2R
E = Z²*E1
(3/2) n R ?t

21. Solid: Resistivity of Metal
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
?~T
Always Real
I = -(c ?t)^2 + d^2

22. Magnetic field due to a segment of wire
? = 1.22?/D
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
U - ts = -tlog(Z)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration

23. Perturbations
H = H_0 + ?H
L = T - V dL/dq = d/dt dL/dqdot
.5 LI²
dQ = dW +dU

24. Complex impedance (expressions for capacitor and inductor)
Z_c = -i/(?C) ; Z_L = i ? L
X_C = 1/(i?C)
dQ = dW +dU
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

25. Resistance - length - area - rho
Z = ?g_i*exp(-E/kT)
L = mr²d?/dt
C_eq = ?C_i
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

26. Mech: Force of Friction
F_f = µ*F_N
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
P1V1 - P2V2 / (? - 1)
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

27. Compton Scattering
? = ?0 root((1-v/c)/(1+v/c))
dU = 0 ? dS = ?dW/T
Infinitely close to equilibrium at all times
?? = h/mc * (1-cos(?))

28. Energy levels from the Coulomb potential
u dm/dt
?~T
?? = h/mc * (1-cos(?))
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)

29. Rotation matrix (2x2)
u dm/dt
I = I_cm + md²
I_z = I_x + I_y (think hoop symmetry)
Cos[?] Sin[?] -Sin[?] Cos[?]

30. Bragg'S Law of Reflection
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
M? = 2dsin(?)
Ct²-x²-y²-z²
NC?T

31. Astro: Aperture Formula (Rayleigh Criterion)
Always Real
? = 1.22?/D
W_A < W_I
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

32. Single Slit Diffraction Intensity
V = V0 + V0 a ?T
I = Im (sinc²(a)) ; a = pai sin(?) / ?
?? = h/mc * (1-cos(?))
<?|O|?>

33. Electromotive Force
DW/dq
?mv
Int ( A . dr) = Int ( del x A) dSurface
F = -2*m(? x r)

34. Effective Potential
ds² = (c*dt)² - ?(x_i)²
F = mv²/r
V(r) + L²2/2mr²
I = I_cm + md²

35. Radiation (Larmor - and another neat fact)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
dQ = dW +dU
T = I?²/2
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

36. EM: Reactance of Inductor
X_L = i?L
dQ = dW +dU
Opposing charge induced upon conductor
S = k ln[O] ; dS = dQ/T

37. Single Slit Diffraction Maximum
P1V1 - P2V2 / (? - 1)
Asin(?) = m?
F = I L X B
T = I?²/2

38. Quant: Commutator Relation [AB -C]
I = V/R exp(-t/RC)
C = 4pe0 ab/(a-b) = inner and outer radii
A[B -C] + [A -C]B
? = 1.22?/D

39. Kepler'S Three Laws
I = I_cm + md²
C_eq = (? 1/C_i)^-1
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

40. Energy in terms of partition function
U = t^2 d/dt (logZ)
W_A < W_I
<?1|?2> = 0 ? Orthogonal
F = µ0 q v I / 2pr

41. A reversible process stays..
S = k ln[O] ; dS = dQ/T
Infinitely close to equilibrium at all times
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.
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point

42. Gibbs Factor
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
I = I_cm + (1/2)m d^2
Exp(N(µ-e)/t)

43. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
B = µ0 I n
Exponentially decreasing radial function
Braking Radiation
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h

44. Double Slit: Interference Minimum - Diffraction Minimum
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
? (t-vx/c²)
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
.5 LI²

45. Anomalous Zeeman Effect

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46. Weighted average (mean and unc. of mean)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

47. Induced EMF of solenoid
I = I_cm + md²
DW/dq
N d flux / dt
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i

48. Solid: Resistivity of Semi-Conductor
1/2 CV²
<T> = -<V>/2
?~1/T
DS = 0 - dQ = 0 - P V^? = constant

49. Relativistic Momentum
I = I_cm + md²
?mv
?s = 0 - ?l = ±1
F = qv×B

50. SR: Total Energy of a Particle
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
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
E = s/e_0
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)