Style questions differently from answers

_psets/1.md

@@ -6,6 +6,7 @@ title: Problem Set 1
 
 ### (a)
 
+{:.question}
 How many atoms are there in a yoctomole?
 
 Yocto is the SI prefix for $$10^{-24}$$. So there are
@@ -18,6 +19,7 @@ atoms in a yoctomole.
 
 ### (b)
 
+{:.question}
 How many seconds are there in a nanocentury? Is the value near that of any important constants?
 
 Nano is the SI prefix for $$10^{-9}$$.
@@ -36,6 +38,7 @@ This is relatively close to $$\pi$$.
 
 ## 2.2
 
+{:.question}
 A large data storage system holds on the order of a petabyte. How tall would a 1 petabyte stack of
 CDs be? How does that compare to the height of a tall building?
 
@@ -54,6 +57,7 @@ stack of CDs would be roughly twice as tall as any other human-built structure.
 
 ## 2.3
 
+{:.question}
 If all the atoms in our universe were used to write an enormous binary number, using one atom per
 bit, what would that number be (converted to base 10)?
 
@@ -67,6 +71,7 @@ as $$10^\num{3e79}$$.
 
 ## 2.4
 
+{:.question}
 Compare the gravitational acceleration due to the mass of the Earth at its surface to that produced
 by a 1 kg mass at a distance of 1 m. Express their ratio in decibels.
 
@@ -82,6 +87,7 @@ $$
 
 ### (a)
 
+{:.question}
 Approximately estimate the chemical energy in a ton of TNT. You can assume that nitrogen is the
 primary component; think about what kind of energy is released in a chemical reaction, where it is
 stored, and how much there is.
@@ -107,6 +113,7 @@ This is off by a factor of about 1.5, which isn't so bad for not knowing what th
 
 ### (b)
 
+{:.question}
 Estimate how much uranium would be needed to make a nuclear explosion equal to the energy in a
 chemical explosion in 10,000 tons of TNT (once again, think about where the energy is stored).
 
@@ -121,6 +128,7 @@ uranium, which is about 650 grams.
 
 ### (c)
 
+{:.question}
 Compare this to the *rest mass energy* $$E = mc^2$$ of that amount of material (Chapter 15), which
 gives the maximum amount of energy that could be liberated from it.
 
@@ -176,6 +184,7 @@ makes it the world's most valuable substance by mass.)
 
 ### (a)
 
+{:.question}
 What is the approximate de Broglie wavelength of a thrown baseball?
 
 A baseball weighs $$1.45^{-1} \si{kg}$$. A major league fastball is around 100 miles per hour, so
@@ -192,6 +201,7 @@ $$
 
 ### (b)
 
+{:.question}
 Of a molecule of nitrogen gas at room temperature and pressure? (This requires either the result of
 Section 3.4.2, or dimensional analysis.)
 
@@ -220,6 +230,7 @@ $$
 
 ### (c)
 
+{:.question}
 What is the typical distance between the molecules in this gas?
 
 The typical distance can be estimated based on the number of particles per volume. If the volume is
@@ -238,6 +249,7 @@ $$
 
 ### (d)
 
+{:.question}
 If the volume of the gas is kept constant as it is cooled, at what temperature does the wavelength
 become comparable to the distance between the molecules?
 
@@ -258,6 +270,7 @@ $$
 
 ### (a)
 
+{:.question}
 The potential energy of a mass m a distance r from a mass $$M$$ is $$−GMm/r$$. What is the escape
 velocity required to climb out of that potential?
 
@@ -270,6 +283,7 @@ $$
 
 ### (b)
 
+{:.question}
 Since nothing can travel faster than the speed of light (Chapter 15), what is the radius within
 which nothing can escape from the mass?
 
@@ -284,6 +298,7 @@ Schwarzschild radius.
 
 ### (c)
 
+{:.question}
 If the rest energy of a mass $$M$$ is converted into a photon, what is its wavelength?
 
 $$
@@ -292,6 +307,7 @@ $$
 
 ### (d)
 
+{:.question}
 For what mass does its equivalent wavelength equal the size within which light cannot escape?
 
 $$
@@ -300,6 +316,7 @@ $$
 
 ### (e)
 
+{:.question}
 What is the corresponding size?
 
 Plugging the above formula for $$M$$ into $$\lambda = h/(M c)$$, we find that
@@ -310,6 +327,7 @@ $$
 
 ### (f)
 
+{:.question}
 What is the energy?
 
 $$
@@ -318,6 +336,7 @@ $$
 
 ### (g)
 
+{:.question}
 What is the period?
 
 $$\tau = 1/f$$ and $$\lambda = c / f = c \tau$$, so
@@ -329,12 +348,14 @@ $$
 
 ## 2.8
 
+{:.question}
 Consider a pyramid of height H and a square base of side length L. A sphere is placed so that its
 center is at the center of the square at the base of the pyramid, and so that it is tangent to all
 of the edges of the pyramid (intersecting each edge at just one point).
 
 ### (a)
 
+{:.question}
 How high is the pyramid in terms of L?
 
 To fit within the square base, the radius of the sphere must be $$L / 2$$. Now imagine rotating the
@@ -346,6 +367,7 @@ lot more tedious.)
 
 ### (b)
 
+{:.question}
 What is the volume of the space common to the sphere and the pyramid?
 
 The sphere is tangent to three points on each wall of the pyramid (the midpoints of each edge). The

_psets/2.md

@@ -6,6 +6,7 @@ title: Problem Set 2
 
 ### (a)
 
+{:.question}
 Derive equation (3.16) (i.e. the Poisson probability density function) from the binomial
 distribution and Stirling’s approximation.
 
@@ -32,7 +33,8 @@ term approaches $$\lambda^k e^{-\lambda}/k!$$ which is the Poisson distribution.
 
 ### (b)
 
-Use it to derive equation (3.18): $$\langle k (k - 1) \cdots (k - m + 1) \rangle = \lambda^m$$ when
+{:.question}
+Use it to derive equation (3.18) ($$\langle k (k - 1) \cdots (k - m + 1) \rangle = \lambda^m$$) when
 k follows the Poisson distribution with average number of events $$\lambda$$.
 
 First, let's verify that $$\langle k \rangle = \lambda$$. This will serve as the base case for an
@@ -63,6 +65,7 @@ $$
 
 ### (c)
 
+{:.question}
 Use (b) to derive equation (3.19): $$\sigma / \langle k \rangle = 1 / \sqrt{\lambda}$$.
 
 To compute $$\sigma$$, we need to know what $$\langle k^2 \rangle$$ is. It can be found using the
@@ -85,6 +88,7 @@ Thus $$\sigma^2 = \langle k^2 \rangle - \langle k \rangle^2 = \lambda (\lambda +
 
 ## (3.2)
 
+{:.question}
 Assume that photons are generated by a light source independently and randomly with an average rate
 N per second. How many must be counted by a photodetector per second to be able to determine the
 rate to within 1%? To within 1 part per million? How many watts do these cases correspond to for
@@ -226,10 +230,12 @@ part of the phase differences averages out to zero.
 
 ## (3.3)
 
+{:.question}
 Consider an audio amplifier with a 20 kHz bandwidth.
 
 ### (a)
 
+{:.question}
 If it is driven by a voltage source at room temperature with a source impedance of 10kΩ how large
 must the input voltage be for the SNR with respect to the source Johnson noise to be 20 dB?
 
@@ -254,13 +260,16 @@ volts.
 
 ### (b)
 
+{:.question}
 What size capacitor has voltage fluctuations that match the magnitude of this Johnson noise?
 
 ### (c)
 
+{:.question}
 If it is driven by a current source, how large must it be for the RMS shot noise to be equal to 1%
 of that current?
 
+
 ## 3.4
 
 This problem is much harder than the others. Consider a stochastic process $$x(t)$$ that randomly
@@ -271,27 +280,33 @@ starts in x = 1.
 
 ### (a)
 
+{:.question}
 Write a matrix differential equation for the change in time of the probability $$p_0(t)$$ to be in
 the 0 state and the probability $$p_1(t)$$ to be in the 1 state.
 
 ### (b)
 
+{:.question}
 Solve this by diagonalizing the 2 × 2 matrix.
 
 ### (c)
 
+{:.question}
 Use this solution to find the autocorrelation function $$hx(t)x(t + \tau)i$$.
 
 ### (d)
 
+{:.question}
 Use the autocorrelation function to show that the power spectrum is a Lorentzian.
 
 ### (e)
 
+{:.question}
 At what frequency is the magnitude of the Lorentzian reduced by half relative to its low-frequency
 value?
 
 ### (f)
 
+{:.question}
 For a thermally activated process, show that a flat distribution of barrier energies leads to a
 distribution of switching times $$p(\tau) \propto 1/\tau$$, and in turn to $$S(f) \propto 1/\nu$$.

_sass/main.scss

@@ -28,3 +28,7 @@ a:visited {
 .current {
   font-weight: bold;
 }
+
+.question {
+    font-style: italic;
+}