PC 242 Midterm Exam
March 5, 2008
Solutions
Instructions: Answer all questions. An equation sheet and a list of constants is provided.
1. An object of mass 10kg is moving to the right at 0.6c in the lab. It explodes into 2 fragments.
Fragment 1 moves to t

PC 242 Assignment 1: Solutions
Instructions: To receive full credit, please explain clearly the steps used to solve each
problem. The reader must be able to follow your logic. Indicate clearly what physical
quantity corresponds to each number used in any

PC 242 Assignment 2: Due in class on Wednesday Jan 30, 2008
1. Textbook chapter 2, problem #16: A particle is moving in the x direction with speed u
and has an energy E and momentum p.
(a) What is the energy and momentum of the particle in a frame moving

PC 242 Assignment 3: Solutions
1. A particle with charge to mass ratio which is 1/1836 the charge to mass ratio of the
electron enters the region between the plates of Thomsons apparatus.
(a) Identify the particle
(b) The particle passes undeflected throu

PC 242 Assignment 5: Due in class on Wednesday March 26, 2008
1. An electron in the n=4 state of a 5nm wide infinite well makes a transition to the
ground state, emitting a photon. What is the wavelength of the photon?
Energy levels in an infinite square

PC 242 Assignment 6: Due on Wednesday April 6, 2016
1. A hydrogen atom is in the 2p state. What is the probability of finding the electron at
twice the Bohr radius a0? What is the average value of the radius in terms of the Bohr
radius? Hint:
k z
z e
dz =

PC 242 Assignment 4: Due in class on Monday March 7, 2016
1. Through what potential difference would an electron have to be accelerated to give it a
de Broglie wavelength equal to the diameter of the hydrogen atom? How does the kinetic
energy of this elec

PC 242 Assignment 6 Solutions
1. A hydrogen atom is in the 2p state. What is the probability of finding the electron at
twice the Bohr radius a0? What is the average value of the radius in terms of the Bohr
radius? Hint:
k z
z e
dz = k! = k(k 1)(k 2).1.
0

PC 242 Assignment 3: Solutions
Instructions: To receive full credit, please explain clearly the steps used to solve each
problem. The reader must be able to follow your logic. Indicate clearly what physical
quantity corresponds to each number used in any

> restart;
>
A procedure to do numerical integartion with Simpson's 1/3 rule
> simpsonOneThird := proc(a,b,n,f)
local h, k;
h := (b-a)/n;
RETURN(evalf(h/3)*(f(a)+f(b)+4*sum(f(a+(2*k-1)*h),k=1.n/2)+2*sum
(f(a+(2*k)*h),k=1.(n-2)/2);
end proc;
simpsonOneThir

PC 242 Assignment 1 Solutions
1. An athlete runs the 100 meter dash at 10 m/s. How much will her watch gain or lose as
compared to ground based clocks during the race?
According to Einsteins theory of special relativity, moving clocks tick slower than
sta

PC 242 Assignment 3: Due in class on Friday Feb 5, 2016
Instructions: To receive full credit, please explain clearly the steps used to solve each
problem. The reader must be able to follow your logic. Indicate clearly what physical
quantity corresponds to

PC 242 Assignment 2: Due in class on Friday Jan 29, 2016
1. An electron moving to the right collides with a positron moving to the left. The two
particles annihilate and produce two gamma ray photons with wavelengths of 0.0011 nm.
Find the velocities of t

PC 242 Assignment 4
1. Through what potential difference would an electron have to be accelerated to give it a
de Broglie wavelength equal to the diameter of the hydrogen atom? How does the kinetic
energy of this electron compare to the ground state energ

PC 242 Assignment 5: Due on Monday March 28th, 2016
1. The nuclear potential that binds protons and neutrons together is often approximated
by a square well with infinite walls. A typical nuclear diameter is 0.0005 Angstroms.
(a) Calculate the wavelength

PC 242 Assignment 5
1. The nuclear potential that binds protons and neutrons together is often approximated
by a square well with infinite walls. A typical nuclear diameter is 0.0005 Angstroms.
(a) Calculate the wavelength of the photon emitted when a pro

PC 242 Assignment 1: Due in class on Monday Jan 18, 2016
Instructions: To receive full credit, please explain clearly the steps used to solve each
problem. The reader must be able to follow your logic. Indicate clearly what physical
quantity corresponds t

PC 242 Assignment 2: Solutions
1. An electron moving to the right collides with a positron moving to the left. The two
particles annihilate and produce two gamma ray photons with wavelengths of 0.0011 nm.
Find the velocities of the electron and positron.

PC 242 Assignment 4: Due in class on Friday Feb 29, 2008
1. If moving at 300m/s, what would be the wavelength of (a) an airplane (b) an electron
Which is more likely to behave like a wave?
If electrons traveling at 3000 km/s were diffracted in a Davisson-

> restart;
f :=
x-> x^2+x+5;
plot(f(x), x=-4.4);
2
f := x x + x + 5
> Df := simplify(D(f);
Df := x 2 x + 1
> na := x -> evalf(x-f(x)/Df(x);
f( x )
na := x evalf x
Df( x )
> x0 := 1+I;
x0 := 1 + I
> x1 := na(x0);
x1 := -0.8461538462 + 1.230769231 I
> x2

> restart;
Implementation of the Gradient Method
for minimization of a function of n variables
> GradientMethodOptimization := proc (f,vars,Pzero,epsilon)
local
P0,Gf,nvars,i,j,gam,GfAtPoint,P0plusGamS0,sizeOf,S0,finterm,sol,ga
mMin,P1;
P0 := Pzero;
Vecto

> restart;
Solve the system f(x,y) = 0, g(x,y) = 0 with Newton's
method
> f := (x,y) -> x^2+y^2-4;
f := ( x, y ) x2 + y2 4
> g := (x,y) -> exp(x)+y-1;
g := ( x, y ) ex + y 1
display the solution graphically
> fp := implicitplot(f(x,y),x=-2.2,y=-2.2):
> gp

> restart;
TRAPEZOIDAL RULE
> a := 0;
b := 1;
f := x-> 1-x^2;
n := 3;
h := (b-a)/n;
(h/2)*(f(a)+f(b)+2*sum(f(a+k*h),k=1.n-1);
evalf(%);
a := 0
b := 1
f := x 1 x2
n := 3
h :=
1
3
35
54
0.6481481481
> a := 0;
b := 1;
f := x-> 1-x^2;
n := 5;
h := (b-a)/n;
(h

Equation sheet
x ! = " (x # vt)
y! = y
z! = z
$ vx '
t ! = "& t # 2 )
% c (
Relativity
1
! =
1 " v2 c2
!t = "!t #
L! =
L
v2
= L 1# 2
"
c
u! =
x
1+ v c 1
1+ v c
=
f source
1! v c "t #
1! v c
f obs =
(!s)
2
= (c!t ) " (!x ) " (!y ) " (!z)
2
2
2
uy =
!
ux "

/
I
is
sheet a list of constants provided.
and
An
Instructrons:Answerall questions. equation
into
l. An objectof massl0kg is movingto the ght at 0.6cin thelab.It explodes 2 fragments.
FragmentI movesto the left at 0.6c, while fragment2 movesto the right a

> restart;
Solution of a boundary-value problem with a finite-difference method
> dsolve(cfw_diff(f(x),x$2)+diff(f(x),x)+f(x)=0,f(0)=0,f(1)=1);
e
(1 / 2)
f( x ) =
e
x
2
sin
3 x
sin
2
3
2
> sol := unapply(rhs(%),x);
e
(1 / 2)
e
( 1 / 2 x )
sol := x