Homework 11

Problem 3

(* solid angle *)
Ω=(area/(d^2)) /.{area->π (r^2)}

moon=Ω /.{d->3.84 (10^8), r->1.74 (10^6)} ;
moon//ScientificForm

sun=Ω /.{d->1.5 (10^11), r->6.96 (10^8)} ;
sun//ScientificForm

(moon/sun)

Problem 4

Clear["Global`*"]

ntar= ((ρ t)/m) /.{ρ->(10.5 (10^3)), t->((10^(-6))), m->(108  *(1.66 (10^(-27))))}

(* solid angle *)
Ω=(area/(d^2))

Ω= Ω /.{area-> 0.1 (10^(-6)), d->1 (10^(-2))}

Nsc = Nin ntar sig Ω/.{Nin-> (10^10),sig->0.5 (10^(-28))}

Problem 5

π/Degree *1.

Plot[Sin[θ/2 Degree],{θ,0,360}]

f[θ_]=(1/((Sin[θ/2 Degree])^4));

LogPlot[f[θ] Sin[θ Degree],{θ,0,180}]

tmp=Integrate[((Sin[θ ])/((Sin[θ/2 ])^4)),θ]

Limit[tmp ,θ->π]

Series[tmp ,{θ,0,1}]

int[a_,b_]:=NIntegrate[f[θ] Sin[θ Degree],{θ,a,b},{ϕ,0,2π}]

total=int[10,180]

Table[xint[a,a+10],{a,10,170,10}]

tab=Table[((int[a,a+10])/total),{a,10,170,10}]

labels=Table[a,{a,10,170,10}]

Length /@ {labels,tab}

BarChart[tab,ScalingFunctions->"Linear",ChartLabels->labels]

BarChart[tab,ScalingFunctions->"Log",ChartLabels->labels]

Problem 5 
Repeat for Hard Sphere

Clear["Global`*"]

π/Degree *1.

f[θ_]=1;

LogPlot[f[θ],{θ,0,180}]

LogPlot[f[θ] Sin[θ Degree],{θ,0,180}]

tmp=Integrate[Sin[θ],{θ,0,π},{ϕ,0,2π}]

int[a_,b_]:=NIntegrate[f[θ] Sin[θ Degree],{θ,a,b},{ϕ,0,2π}]

total=int[0,180]

Table[xint[a,a+10],{a,00,170,10}]

tab=Table[((int[a,a+10])/total),{a,00,170,10}]

labels=Table[a,{a,00,170,10}]

Length /@ {labels,tab}

BarChart[tab,ScalingFunctions->"Linear",ChartLabels->labels]

BarChart[tab,ScalingFunctions->"Log",ChartLabels->labels]

Problem 6

Clear["Glboal`*"]

Part a

lum = (10.^34) (1/(cm^2))(1/sec)

higgsCS=50. pb //.{pb ->(10^(-12)) barn, barn ->(10^(-28)) (m^2),m->(10^2)cm}

hrate= lum  higgsCS

1/hrate

Part b

UnitConvert[Quantity[1,"Years"],"Seconds"]

oneYear=1 year( ((365.25 days)/(1 year)))( ((24 hour)/(1 days)))( ((60 min)/(1 hour)))( ((60 sec)/( 1 min)))

hPerYear=(1/3)hrate oneYear;
hPerYear //EngineeringForm

Part c

rate=40. (10^6)(1/sec)

normalPerYear=(1/3)rate oneYear

Part d

(normalPerYear/hPerYear) //EngineeringForm

Part e

rate

rate  //EngineeringForm

1/rate

1/rate //EngineeringForm

c=3.0 10^8 (meter/sec);

(c/rate)

(c/rate)(((3.3 feet)/(1 meter)))