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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. Volumetric Expansion
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
V = V0 + V0 a ?T
? (t-vx/c²)
I_z = I_x + I_y (think hoop symmetry)

2. Atom: Positronium Reduced Mass
Exponentially decreasing radial function
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
Exp(N(µ-e)/t)
µ = m_e/2

3. Magnetic Field For Current in Long Wire
S = k ln[O] ; dS = dQ/T
W_A < W_I
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
µ0 I / 2pR

4. Stark Effect
? = h/mv
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
F = mv²/r
F = -2*m(? x r)

5. EM: Method of Images
V = -L di/dt
E = <?| H |?>
4H + 2e- ? He +2? + 6?
Opposing charge induced upon conductor

6. Thermo: Adiabatic Work vs Isothermal Work
(° of Freedom)kT/2
?mv
W_A < W_I
Dv = -udm/m - v = v0 + u ln(m0/m)

7. Stoke'S Theorem
Int ( A . dr) = Int ( del x A) dSurface
F = f* (c+v_r)/(c+v_s)
F = I L X B
I = I_0 Cos[?]^2

8. Doppler Shift for light
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
F = s * T4
? = ?0 root((1-v/c)/(1+v/c))
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

9. Pauli matrices
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
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
F_f = µ*F_N

10. Relativistic Energy
F = R/2
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
V = V0 + V0 a ?T
?mc²

11. Electromotive Force
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.
DW/dq
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
DW = P dV

12. Biot-Savart law
4H + 2e- ? He +2? + 6?
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
A[B -C] + [A -C]B
X_C = 1/(i?C)

13. How to derive cylcotron frequency
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
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
Int ( A . dr) = Int ( del x A) dSurface
qvb = mv²/R

14. Rocket Thrust
?mc²
u dm/dt
X_L = i?L
?max = 2.898 x 10 -³ / T

15. Force/length between two wires
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
F = -2*m(? x r)
µ0 I1I2 / (2pd)
P/A = s T^4

16. Gibbs Factor
Exp(N(µ-e)/t)
J = E s - s = Conductivity - E = Electric field
<T> = 1/2 * <dV/dx>
µ0 I / 2R

17. Mech: Rotational Energy
F = mv²/r
T = I?²/2
Measurements close to true value
?s = 0 - ?l = ±1

18. Mech: Force of Friction
?~1/T
N²/Z (m_elec/m_red)
F_f = µ*F_N
Exponentially decreasing radial function

19. EM: SHO (Hooke)
N d flux / dt
F = f* (c+v_r)/(c+v_s)
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
ma + kx = 0

20. QM: de Broglie 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.
Measurements close to mean
?= h/v(2mE)
I = Im (sinc²(a)) ; a = pai sin(?) / ?

21. Compton Scattering
Ct²-x²-y²-z²
?? = h/mc * (1-cos(?))
I_z = I_x + I_y (think hoop symmetry)
F = µ0 q v I / 2pr

22. Time Lorentz Transformation
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
µ = m_e/2
? = ?0 root((1-v/c)/(1+v/c))
? (t-vx/c²)

23. Single Slit Diffraction Maximum
Asin(?) = m?
? (t-vx/c²)
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
N d flux / dt

24. De Broigle Wavelength
V = -L di/dt
dU = 0 ? dS = ?dW/T
?_max = b/T
? = h/mv

25. Effective Potential
M? = 2dsin(?)
Cos[?] Sin[?] -Sin[?] Cos[?]
V(r) + L²2/2mr²
Braking Radiation

26. Energy in Inductor
.5 LI²
<?|O|?>
ds² = (c*dt)² - ?(x_i)²
µ0 I / 2R

27. Expectation value of the energy of state |?>
E = <?| H |?>
µ0 I / 2R
V = V0 + V0 a ?T
C = 4pe0 ab/(a-b) = inner and outer radii

28. Lagrangian and Lagrange'S equation
Measurements close to true value
V = V0 + V0 a ?T
L = T - V dL/dq = d/dt dL/dqdot
S_mean = s/Sqrt[N]

29. Hamiltonian and Hamilton'S equations
? exp(-e/t)
µ = Current * Area T = µ x B
dU = 0 ? dS = ?dW/T
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i

30. Kepler'S Three Laws
Z = ?g_i*exp(-E/kT)
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
NC?T
L = mr²d?/dt

31. Rayleigh'S Criterion
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
H = H_0 + ?H
? = ?0 root((1-v/c)/(1+v/c))
Sin(?) = ?/d

32. Error in the mean if each measurement has the same uncertainty s
I_z = I_x + I_y (think hoop symmetry)
S_mean = s/Sqrt[N]
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.
P1V1 - P2V2 / (? - 1)

33. Virial Theorem
<T> = 1/2 * <dV/dx>
Const: 2t = (n +.5)? Destructive 2t = n?
Sin(?) = ?/d
<?1|?2> = 0 ? Orthogonal

34. EM: Lorentz Force
F = qv×B
F = I L X B
E = s/e_0
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

35. Magnetic Dipole Moment and Torque
µ = Current * Area T = µ x B
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.
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
T^2 = k R^3 - k=constant

36. Energy in terms of partition function
U = t^2 d/dt (logZ)
E = Z²*E1
L = T - V dL/dq = d/dt dL/dqdot
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

37. Lab: Accuracy of Measurements
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
X_C = 1/(i?C)
? (t-vx/c²)
Measurements close to true value

38. Current in resistor in RC circuit
PdV +dU
(3/2) n R ?t
I = V/R exp(-t/RC)
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.

39. Charge in Capacitor
Always Real
C_eq = (? 1/C_i)^-1
?_max = b/T
Q = CVexp(-t/RC)

40. Angular momentum operators L^2 and L_z
S = k ln[O] ; dS = dQ/T
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
X_L = X_C or X_total = 0
I_z = I_x + I_y (think hoop symmetry)

41. Quant: Expectation Value
? = ?0 root((1-v/c)/(1+v/c))
C_eq = ?C_i
.5 CV²
<?|O|?>

42. Relativistic length contraction
Infinitely close to equilibrium at all times
L = L_0 Sqrt[1-v^2/c^2]
<T> = -<V>/2
U = t^2 d/dt (logZ)

43. Selection rules for atomic transitions
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
P² ~ R³
Exponentially decreasing radial function
L = T - V dL/dq = d/dt dL/dqdot

44. Weighted average (mean and unc. of mean)
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
N²/Z (m_elec/m_red)
<T> = -<V>/2

45. Bragg'S Law of Reflection
M? = 2dsin(?)
C = 4pe0 ab/(a-b) = inner and outer radii
Exp(N(µ-e)/t)
T^2 = k R^3 - k=constant

46. Heat added
Z = ?g_i*exp(-E/kT)
NC?T
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
<T> = 1/2 * <dV/dx>

47. Mech: Virial Theorem
ma + kx = 0
Z_c = -i/(?C) ; Z_L = i ? L
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
<T> = -<V>/2

48. Planck Radiation Law
µ0 I / 2R
W_A < W_I
? = 1.22? / d
Hbar*?³/(p²c³exp(hbar?/t)-1)

49. Rocket Equation
Dv = -udm/m - v = v0 + u ln(m0/m)
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
? = h/p
?s = 0 - ?l = ±1

50. Atom: Hydrogen Wave Function Type
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
Exponentially decreasing radial function
P² ~ R³