relativity!!!!!!!!!!!!!!!
waves and stuff!!!!!!
schrodinger -- 1D!!!!
schrodinger -- 3D!!!!
mystery category!!!!
100
A snail is moving at a speed of (21/29)c. What is its Lorentz factor, ɣ?
(29/20) or 1.45
100
What is the formula for the de Broglie wavelength?
λ = h/p
100
What is the formula for the probability of quantum tunneling?
P ≈ e-2αL where α=sqrt[2m(U0-E)]/ħ
100
What are the letters representing l=0, l=1, l=2, l=3, l=4, l=5, and l=6?
s p d f g h i
0 1 2 3 4 5 6
100
Use Mathematica to integrate ∫0∞ x15e-xdx. What is the answer? How would you integrate this by hand?
Mathematica gives me 1,307,674,368,000. To integrate it by hand, you'd need to integrate by parts about 15 times.
200
Spencer's fencing blade is 1m long. If Spencer swings the blade forwards at a speed of (24/25)c, how long is their fencing blade?
0.28m, or 28 cm
200
Is this function odd or even?
Odd: f(-x) = - f(x)
200
What is the time-independent Schrodinger equation?
d2Ψ/dx2 = (2m/ħ2)[U(x)-E]Ψ
200
What is the 3 dimensional version of the time independent Schrodinger equation?
d2Ψ/dx2 + d2Ψ/dy2 + d2Ψ/dz2 = (2M/ħ2)[U-E]Ψ
200
f(x, y, z) = ln(x)*sin(y/z)
Find all three partial derivatives.
df/dx = (1/x)*sin(y/z)
df/dy = ln(x)*(1/z)*cos(y/z)
df/dz = ln(x)*(-y/z^2)*cos(y/z)
300
There are 2 hours allotted for the final exam in Rob Owen's frame of reference. If he is running around the room at (15/17)c while you take your final, how long will you have to complete the final in your reference frame?
4.25 hours
300
An electron in a Li2+ ion drops from the 5th energy level to the 2nd energy level. What wavelength of light is emitted?
48 nm
300
Two straight wires are separated by a 4 nm gap. The potential energy in the gap is 3 eV higher than the potential energy in a wire. Find the probability that an electron tunnels into the other wire.
(Taylor 7.54)
P ≈ 1.5 * 10-31 (at least I hope... my calculator's messed up this type of problem before)
300
For a given L = √(l(l+1)) ħ, what is the largest allowed value of Lz? Prove this is always less than or equal to L.
(Taylor 8.26)
Largest allowed value of Lz: lħ
There are probably lots of ways to go about the proof. I argued that L = √(l2+l)ħ and Lz = √(l2+0)ħ. Since l≥0, then L≥Lz.
300
Trig identity race! How many trig identities can you write on the board in two minutes?
:)
400
I was skateboarding at 0.5c when I lost my balance and fell forwards at 0.4c!! Oh no!! What is my speed relative to the ground?
0.75c
400
A double slit with d = 0.1 mm is located 1.00 m away from a screen, and 750 nm light falls on the slit. What is the distance of the 3rd intensity maximum from the center of the screen?
~2.25 cm
400
Find the normalization constant A for the n=0 simple harmonic oscillator wave function, Ae^(-x2/2b2).
(Hint: ∫0∞ e^(-λx2)dx = √(π/4λ) )
(Taylor 7.50)
A = (πb2)-1/4
400
Given the radial probability density function P1s = (((1/√(πa3))e-r/a)2)*4πr2 where a is the Bohr radius, calculate the expectation value of the radius, <r> = ∫0∞ rP(r)dr.
<r> = (3/2)a
400
An electron in a 4f orbital is placed in a magnetic field of magnitude 1.0 T. How many 4f energy levels are there now? What is the energy difference between the highest and the lowest energy level?
There are 7 energy levels. The difference between the highest and lowest energy is about 3.5*10^-5 eV.
500
A piece of bread with peanut butter flies towards a piece of bread with jelly. Both have a mass of 50g. One has a speed of +(3/5)c, and one has a speed of -(3/5)c. They collide to form a PB&J. What is the mass of the PB&J?
125 g
500
A particle's wavefunction squared is given by |ψ(x)|2=(3/4)(1-x^2). What is the uncertainty in its position?
Δx = 1/√5
500
Verify that the simple harmonic oscillator wave function for n=1, A1(x/b)e^(-x2/2b2) where b=sqrt(ħ/mω), satisfies the Schrodinger equation with energy E=(3/2)ħω.
(shuffling numbers around)
500
The radial wave function R1s is given by (2/√a3)e-r/a where a is the Bohr radius. Find the radius at which the probability is at a maximum.
The probability is at a maximum at r=a.
500
The period of a pendulum is given by T=c*(L^a)*(g^b), where T is the period, L is the length, g is gravity, and a, b, and c are some constants. Derive the values of a and b using dimensional analysis. What should the formula for the period be?
a=1/2, b=-1/2 => T=c*√ (L/g)
This is indeed the correct formula for the period of a pendulum. The constant c ends up being 2π.