1. Joe estimates that on his drive to work, he sees one flattened possum
on the road about every three weeks.

Mike, who has just begun to ride to work with him, has never
seen this, having come from Arizona where

they run over skunks instead. How many weeks will Mike have to ride
with Joe to have a 90% confidence

of seeing at least one possum on the road?

The mean is 1/3 per week, and with small numbers, Poisson statistics are appropriate.

Calculating the probability of seeing no possums and setting it equal to 10%:

0.1 = exp(-a)

ln(.1)=-a; a= 2.30

np=a; n=a/p=3a= 6.91 so almost 7 weeks to be 90% sure.

2. The element potassium is reported to have one of the larger atomic
radii, and may be a counterexample

to Rohlf's universal 0.3 nm atom. If the density of solid is 0.86 gm/cm3
and its molar mass is 39.1 grams,

calculate the atomic radius. State clearly any assumptions you make.

The volume per atom can be calculated from v= molar mass/(density*avogadro's
number)

volume = (.0391 kg/mole)/(860 kg/m^3*6.022e23 atoms/mole) =
7.55E-29 m^3/atom

Taking the volume as a simple cube gives diameter = 4.2E-10
m = 0.423 nm

3. Lay out all the possible ways that 3 particles can have 4 units of
energy, and calculate the number of

states associated with each configuration.

Energy =
0 1 2 3 4 Weighting

Number of part. 2 0 0 0 1
3

1 1 0 1 0 6

1 0 2 0 0 3

0 2 1 0 0 3

4. Protons from the solar wind get placed into spiral paths toward the
North pole by the Earth's magnetic

field, contributing to auroral displays. If the Earth's magnetic field
is 0.5 E-4 Tesla, and the

component of the proton's velocity perpendicular to the that field
is 1E4 m/s, what is the radius of the

circular crosssection of the spiral path?

mv^2/r=qvB, r=mv/qB= (1.67e-27kg*1e4 m/s)/(1.6e-19C*0.5e-4T)= 2.0875 m

5. Deuterium-tritium fusion to form an alpha particle and a neutron
offers probably the greatest hope for

generating electricity by nuclear fusion. The mass energies of the
constituents are given below.

deuterium 1.8756 GeV

tritium 2.8089 GeV

alpha 3.7274 GeV

neutron 0.9396 GeV

Calculate the energy yield of the fusion process and the speed of the
lone neutron if it receives all

energy of the process.

Mass difference = 0.0175 GeV= 2.8E-12 joules

v=sqrt(2E/m)=sqrt(2*2.8e-12J/1.6749e-27)= 5.78E+07 m/s
= 0.19c

6. You are told that air molecules collide about 5 billion times per
second. Does than make sense?

Calculate the collision rate assuming an average molar mass of 29,
a temperature 0°C, and atmospheric

pressure. State any assumptions made.

Average speed = sqrt(8kT/pi*m) = sqrt(8*1.38e-23*273/(Pi()*29*1.66e-27))=
446.41 m/s

Mean free path= volume per atom/cross section for collision = 0.0224m^3/(pi*(.3nm)^2*6.02e23*1e-18)

mean free path= 1.316E-07 m

Rate of collisions = average speed/mean free path = 3.39E+09 /s