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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. Atom: Bohr Theory Ionization
Const: 2t = (n +.5)? Destructive 2t = 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
E = Z²*E1
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

2. EM: Parallel Capacitance
E = <?| H |?>
P/A = s T^4
C_eq = ?C_i
Hbar*?³/(p²c³exp(hbar?/t)-1)

3. Planck Radiation Law
P² ~ R³
H = H_0 + ?H
Hbar*?³/(p²c³exp(hbar?/t)-1)
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

4. Thermo: Blackbody Radiation
X_L = i?L
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
F = s * T4
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)

5. Selection rules for atomic transitions
ma + kx = 0
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
Cv = dE/dT = 3R
v(mean)

6. Dulong Petit Law
Cv = dE/dT = 3R
F_f = µ*F_N
F = qv×B
?s = 0 - ?l = ±1

7. Energy levels from the Coulomb potential
I ' = I cos²(?)
N d flux / dt
? = h/p
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)

8. Quant: Eigenvalue of Hermitian Operator
Isentropic
F = µ0 q v I / 2pr
Always Real
? = 5/3

9. Poisson distribution (µ and s)
<?1|?2> = 0 ? Orthogonal
µ=s^2
Cos[?] Sin[?] -Sin[?] Cos[?]
Q = CVexp(-t/RC)

10. EM: Method of Images
Opposing charge induced upon conductor
KE = 1/2 * µ (dr/dt)² L = µ r x v
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
F = f* (c+v_r)/(c+v_s)

11. Thermo: Isothermal
T^2 = k R^3 - k=constant
?mc²
dU = 0 ? dS = ?dW/T
H = H_0 + ?H

12. Self Inductance
?= h/v(2mE)
V = -L di/dt
KE = 1/2 * µ (dr/dt)² L = µ r x v
NC?T

13. Doppler Shift for light
? = ?0 root((1-v/c)/(1+v/c))
DS = 0 - dQ = 0 - P V^? = constant
qvb = mv²/R
Hbar*?³/(p²c³exp(hbar?/t)-1)

14. Force on a wire in magnetic field
F = I L X B
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
Sin(?) = ?/d
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

15. Bernoulli Equation
P +1/2 ? v² + ?gh = Constant
H = H_0 + ?H
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.
?_max = b/T

16. Induced EMF of solenoid
Dp/dt = L / (t ?V)
P/A = s T^4
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
N d flux / dt

17. Triplet/singlet states: symmetry and net spin
J/(ne) n: atom density
Const: 2t = (n +.5)? Destructive 2t = n?
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
ds² = (c*dt)² - ?(x_i)²

18. Work in a capacitor
1/2 CV²
?s = 0 - ?l = ±1
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
? = h/mv

19. Perturbations
H = H_0 + ?H
4H + 2e- ? He +2? + 6?
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
B = µ0 I n

20. How to derive cylcotron frequency
Cos[?] Sin[?] -Sin[?] Cos[?]
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
qvb = mv²/R
H = H_0 + ?H

21. Wein'S Displacement Law
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
?max = 2.898 x 10 -³ / T
?= h/v(2mE)
I = V/R exp(-t/RC)

22. Adiabatic means
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
?_max = b/T
Isentropic
? = h/p

23. Radiation (Larmor - and another neat fact)
F = -2*m(? x r)
Const: 2t = (n +.5)? Destructive 2t = n?
T^2 = k R^3 - k=constant
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration

24. EM: AC Resonance
E = Z²*E1
X_L = X_C or X_total = 0
F = s * T4
dU = 0 ? dS = ?dW/T

25. 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
1/vLC
M? = 2dsin(?)
Dp/dt = L / (t ?V)

26. Partition Function
? exp(-e/t)
V(r) + L²2/2mr²
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
Infinitely close to equilibrium at all times

27. Relativistic length contraction
L = L_0 Sqrt[1-v^2/c^2]
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
I = I_cm + md²
F = qv×B

28. Stoke'S Theorem
Const: 2t = (n +.5)? Destructive 2t = n?
J = E s - s = Conductivity - E = Electric field
Int ( A . dr) = Int ( del x A) dSurface
Z²/n² (m_red/m_elec)

29. Quant: Orthogonality of States
<?1|?2> = 0 ? Orthogonal
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
I = I_0 Cos[?]^2

30. Single Slit Diffraction Maximum
I = I_0 Cos[?]^2
Asin(?) = m?
S_mean = s/Sqrt[N]
P1V1 - P2V2 / (? - 1)

31. EM: SHO (Hooke)
?= h/v(2mE)
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
ma + kx = 0
<T> = -<V>/2

32. Energy in a Capacitor
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
.5 CV²
qvb = mv²/R
?? = h/mc * (1-cos(?))

33. De Broigle Wavelength
Z = ?g_i*exp(-E/kT)
P² ~ R³
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
? = h/mv

34. Source Free RL Circuit
M? = 2dsin(?)
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
Sin(?) = ?/d
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

35. Force exerted on charge by long wire
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
? exp(-e/t)
F = µ0 q v I / 2pr
dU = 0 ? dS = ?dW/T

36. Energy in terms of partition function
U = t^2 d/dt (logZ)
T = I?²/2
I = I_0 Cos[?]^2
Exp(N(µ-e)/t)

37. Solid: Resistivity of Metal
L = mr²d?/dt
? exp(-e/t)
?~T
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length

38. Wein'S displacement law for blackbodies (? and T)
?_max = b/T
?~1/T
Q = CVexp(-t/RC)
? = 5/3

39. De Broglie wavelength
Infinitely close to equilibrium at all times
F = I L X B
U - ts = -tlog(Z)
? = h/p

40. Current in resistor in RC circuit
I = V/R exp(-t/RC)
M? = 2dsin(?)
Dp/dt = L / (t ?V)
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

41. Thermo: 1st Law
dQ = dW +dU
Dp/dt = L / (t ?V)
Z²/n² (m_red/m_elec)
? exp(-e/t)

42. Quant: Commutator Relation [AB -C]
B = µ0 I n
A[B -C] + [A -C]B
E = <?| H |?>
?~1/T

43. Work done on a gas
P +1/2 ? v² + ?gh = Constant
1/2 CV²
µ0 I / 2pR
DW = P dV

44. Coriolis Force
C_eq = (? 1/C_i)^-1
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
F = -2*m(? x r)
I = I_cm + md²

45. Volumetric Expansion
?~1/T
V = V0 + V0 a ?T
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
P1V1 - P2V2 / (? - 1)

46. Mean electron drift speed
1/2 CV²
J/(ne) n: atom density
Hbar*?³/(p²c³exp(hbar?/t)-1)
(° of Freedom)kT/2

47. EM: Electromagnetic inertia
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
J = ? Fdt
Faraday/Lenz: current inducted opposes the changing field

48. Virial Theorem
<T> = -<V>/2
?s = 0 - ?l = ±1
Ct²-x²-y²-z²
<T> = 1/2 * <dV/dx>

49. Delta Function Potential - type of WF
L = L_0 Sqrt[1-v^2/c^2]
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
.5 LI²
F = qv×B

50. Helmholtz Free Energy
E²-p²c²
F = R/2
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
U - ts = -tlog(Z)