Physics 3401, Homework Quiz 1

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