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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. Law of Mass Action
Isentropic
?? = h/mc * (1-cos(?))
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
? = h/p

2. Lensmaker Equation - Thin Lens
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
ds² = (c*dt)² - ?(x_i)²
J = ? Fdt
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

3. Spherical Capacitor Equation
? = ?0 root((1-v/c)/(1+v/c))
?s = 0 - ?l = ±1
C = 4pe0 ab/(a-b) = inner and outer radii
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas

4. Quant: Orthogonality of States
? = h/mv
Isentropic
<?1|?2> = 0 ? Orthogonal
Braking Radiation

5. Gibbs Factor
N d flux / dt
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
Exp(N(µ-e)/t)

6. Doppler shift for light
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
T^2 = k R^3 - k=constant
µ0 I / 2pR
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

7. Polarizers - intensity when crossed at ?
U = t^2 d/dt (logZ)
Ct²-x²-y²-z²
I = I_0 Cos[?]^2
W_A < W_I

8. Kepler'S third law (T and R)
E = <?| H |?>
F = mv²/r
L = L_0 Sqrt[1-v^2/c^2]
T^2 = k R^3 - k=constant

9. Lagrangian and Lagrange'S equation
L = T - V dL/dq = d/dt dL/dqdot
I_z = I_x + I_y (think hoop symmetry)
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
Sin(?) = ?/d

10. Mean electron drift speed
I = I_cm + md²
J/(ne) n: atom density
Measurements close to true value
0

11. Heat added
L = mr²d?/dt
<?1|?2> = 0 ? Orthogonal
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
NC?T

12. Mech: Centripetal Force
F = mv²/r
<T> = 1/2 * <dV/dx>
KE = 1/2 * µ (dr/dt)² L = µ r x v
Q = CVexp(-t/RC)

13. QM: de Broglie Wavelength
P1V1 - P2V2 / (? - 1)
I = I_cm + (1/2)m d^2
?= h/v(2mE)
? = h/mv

14. Atom: Bohr Formula
I = Im (sinc²(a)) ; a = pai sin(?) / ?
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
? = 5/3
dU = 0 ? dS = ?dW/T

15. A reversible process stays..
Infinitely close to equilibrium at all times
µ0 I / 2R
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
U = t^2 d/dt (logZ)

16. Boltzmann / Canonical distribution
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
Asin(?) = m?
E = s/e_0
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

17. 3 Laws of Thermo
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
Ct²-x²-y²-z²
M? = 2dsin(?)
DW/dq

18. Biot-Savart law
µ0 I / 2R
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
qvb = mv²/R
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

19. EM: AC Resonance
X_L = X_C or X_total = 0
T^2 = k R^3 - k=constant
?s = 0 - ?l = ±1
? = 1.22?/D

20. Planck Radiation Law
Z²/n² (m_red/m_elec)
Always Real
F = -2*m(? x r)
Hbar*?³/(p²c³exp(hbar?/t)-1)

21. Error in the mean if each measurement has the same uncertainty s
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
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
S_mean = s/Sqrt[N]

22. EM: Electric Field inside of Conductor
Const: 2t = (n +.5)? Destructive 2t = n?
ds² = (c*dt)² - ?(x_i)²
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
0

23. Bragg'S Law of Reflection
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
M? = 2dsin(?)
V(r) + L²2/2mr²
µ0 I / 2pR

24. Thermo: Average Total Energy
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
E = <?| H |?>
(° of Freedom)kT/2
µ=s^2

25. Magnetic Field of a long solenoid
µ = Current * Area T = µ x B
C_eq = (? 1/C_i)^-1
DW/dq
B = µ0 I n

26. Rotation matrix (2x2)
Isentropic
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
Cos[?] Sin[?] -Sin[?] Cos[?]
J = ? Fdt

27. Lab: Precision of Measurements
Measurements close to mean
Z = ?g_i*exp(-E/kT)
J = E s - s = Conductivity - E = Electric field
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

28. Bohr Model: Energy
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
Z²/n² (m_red/m_elec)
X_L = X_C or X_total = 0

29. Selection Rules
<T> = 1/2 * <dV/dx>
?s = 0 - ?l = ±1
Exp(N(µ-e)/t)
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

30. Virial Theorem
N d flux / dt
? = h/mv
<T> = 1/2 * <dV/dx>
? = 5/3

31. Triplet/singlet states: symmetry and net spin
DS = 0 - dQ = 0 - P V^? = constant
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
u dm/dt
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0

32. Work (P - V)
L = L_0 Sqrt[1-v^2/c^2]
P1V1 - P2V2 / (? - 1)
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

33. Electromotive Force
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
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
DW/dq
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

34. Doppler Shift for light
? = ?0 root((1-v/c)/(1+v/c))
NC?T
Isentropic
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

35. First law of thermodynamics (explain direction of energy for each term)
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
H = H_0 + ?H

36. EM: Parallel Capacitance
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
C_eq = ?C_i
I = V/R exp(-t/RC)
Exponential - E = -ma²/2hbar² - a is strength of delta wellt

37. Source Free RL Circuit
S = k ln[O] ; dS = dQ/T
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
J = ? Fdt

38. Clausius-Clapeyron Equation
F_f = µ*F_N
Dp/dt = L / (t ?V)
0
V = V0 + V0 a ?T

39. Lab: Accuracy of Measurements
Measurements close to true value
M? = 2dsin(?)
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
C = 4pe0 ab/(a-b) = inner and outer radii

40. Stefan-Boltzmann law for blackbodies (power per area and T)
P/A = s T^4
µ=s^2
dQ = dW +dU
?= h/v(2mE)

41. Effective Potential
Z = ?g_i*exp(-E/kT)
µ = m_e/2
V(r) + L²2/2mr²
L = mr²d?/dt

42. Force on a wire in magnetic field
F = I L X B
1/2 CV²
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
H = H_0 + ?H

43. Bohr Model: Radii
Dp/dt = L / (t ?V)
I = I_cm + (1/2)m d^2
N²/Z (m_elec/m_red)
Always Real

44. EM: Reactance of Capacitor
(3/2) n R ?t
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
X_C = 1/(i?C)
µ0 I1I2 / (2pd)

45. Energy levels from the Coulomb potential
F = R/2
PdV +dU
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
I = I_cm + md²

46. Wein'S Displacement Law
v(mean)
?max = 2.898 x 10 -³ / T
Measurements close to mean
I = V/R exp(-t/RC)

47. Magnetic Field For Current in Long Wire
S = k ln[O] ; dS = dQ/T
N²/Z (m_elec/m_red)
µ0 I / 2pR
?? = h/mc * (1-cos(?))

48. Angular momentum - Central Force Motion
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
F = R/2
L = mr²d?/dt
Sin(?) = ?/d

49. Selection rules for atomic transitions
Exponentially decreasing radial function
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
Measurements close to mean
Isentropic

50. Compton Scattering
?? = h/mc * (1-cos(?))
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
H = H_0 + ?H
Dp/dt = L / (t ?V)