1. (20 points)
(a) (10 points) Consider two inertial reference frames. When an observer in each
frame measures the following quantities, which measurements made by the two
observers will definitely yield the same results? (You can circle your answers
or w

Chapter 4: Quan.za.on of light
Quan.zed means it can occur only in certain
discrete amounts
Quan.zed is the opposite of con.nuous
Examples: Eggs are quan.zed, gasoline is not.
Nor is buCer. Black beans are q

Special Rela*vity
Time dila*on
Last *me, you learned that t = *to
Where to is proper *me. It is the *me between two events
measured at the same loca+on in a par*cular frame of
reference.
If frame t

Chapter 6: Wave Nature of Ma2er
Classically, light is a wave. Quantum
mechanics says its also [email protected] (photons).
Classically, an electron is a [email protected] Louis
De Broglie proposed its also a wave.
[email protected] duali

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
2.0 kg mass is moving along the x-axis. The potential energy curve as a
function of position is shown in the figure. The kinetic energy of the object at
the origin is 12 J

30) Two
objects of the same mass move along the same line in opposite directions. The
first mass is moving with speed v. The objects collide, stick together, and move with
speed 0.100v in the direction of the velocity of the first mass before the collisio

47) The
force on a 3.00-kg object as a function of position is shown in the figure. If an
object is moving at 2.50 m/s when it is located at x = 2.00 m, what will its speed be
when it reaches x = 8.00 m? (Assume that the numbers on the graph are accurate

19) How
much work is done by 3.00 mol of ideal gas when it triples its volume at a
constant temperature of 127C? The ideal gas constant is R = 8.314 J/mol K.
A) 15.3 kJ
B) 9.97 kJ
C) 1.20 kJ
D) 11.0 kJ
E) 12.7 kJ
19)
Answer: D
20) An
ideal gas in a balloo

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
6)
Consider two cylinders of gas identical in all respects except that one contains
oxygen O2 and the other helium He. Both cylinders initially contain the same
volume of

50) Ekapluto
is an unknown planet that has two moons in circular orbits. The table
summarizes the hypothetical data about the moons.
Moon A
Moon B
Mass
4.0 1020 kg
1.5 1020 kg
Radius
2.0 105 m
The orbital period of Moon B is closest to
A) 6.0 106 s.
B) 6.

the figure, a block of mass m is moving along the horizontal frictionless
surface with a speed of 5.70 m/s. If the slope is 11.0 and the coefficient of
kinetic friction between the block and the incline is 0.260, how far does the
block travel up the incli

Chapter 2 Clicker Question 1
1.
Which of the following is true for massless particles?
a.
b.
c.
d.
their momentum is given by p=E/c,
they move at the speed of light,
they cannot come to rest,
all of the above.
Chapter 2 Clicker Question 1
1.
Which of the

Chapter 1 Clicker Ques1on
5.
Which is measured in the rest frame of the object or events?
a.
b.
c.
d.
proper mass
proper 1me
proper length
all of the above.
Chapter 1 Clicker Answer
5.
Which is measured in the rest frame of the object or events?

Chapter 7
Rounded Well
"x
#" x
! (x) = Ae + Be
outside well
! (x) = F sinkx + G coskx inside well
"x
#" x
! (x) = Ae + Be
outside well
! (x) = F sinkx + G coskx inside well
Harmonic Oscillator
Diatomic molecule
poten8al
Harmonic Oscillator

Chapter 7
The Schroedinger Equation in One Dimension
In classical mechanics the state of motion of a particle is specified by the particles
position and velocity. In quantum mechanics the state of motion of a particle is given
by the wave function. The go

Chapter 8
The Three Dimensional Schroedinger Equation and Partial Derivatives
In one dimension the Schroedinger equation has the form
d2 (x)
2M
= 2 [U (x) E] (x)
2
dx
h
(1)
where we use capital M for the particles mass since we will use lowercase m later

Physics 51A: Modern Physics
Prof. Clare Yu
email: [email protected]
phone: 949-824-6216
Office: 210E RH
CHAPTER 1
Introduction
Have you ever watched a horror or science fiction movie where everything starts out
very normal and ordinary, but then strange and biz

Chapter 2: Relativistic Mechanics
Introduction
We know that Newtons laws of motion hold and are invariant in inertial frames of
reference that are related by the Galilean transformation. But it is the Lorentz transformation rather than the Galilean transf

Chapter 6
The Quantum Wave Function
Lets just get to the point: Quantum mechanics represents a particle as a wavefunction: (~r, t). What does a wavefunction mean physically? It means that the probability
that a particle is located in a volume dV is |(~r,

Midterm Exam
Midterm exam is on Thursday May 5 from 12:30 -1:50 pm.
Please bring student IDs.
Covers chapters 1-4.
5 quesHons.
Old exam with soluHons posted online.
Physical constants given, formulas given.
Formula sheet will be provided and is pos

Chapter 5
Example
The helium atom has 2 electronic energy levels: E3p = 23.1 eV and E2s = 20.6 eV
where the ground state is E = 0. If an electron makes a transition from 3p to 2s, what
is the wavelength of the photon emitted?
So
=
E = E3p E2s = 2.5 eV
(1)

Chapter 3: Sections 3.1-3.7
Elements: Greeks asked, What are the most
basic substances from which others are
formed? (Important to ask the right question)
Atoms: Greeks asked, What are the smallest,
indivisible particles?
Law of definite proportions:

2R
Figure 1: Cross Section.
Chapter 3
3.8 Mean Free Path and Diffusion
In a gas, the molecules collide with one another. Momentum and energy are conserved
in these collisions, so the ideal gas law remains valid.
The mean free path is the average distance

Chapter 4
Example of Bragg Law
The spacing of one set of crystal planes in NaCl (table salt) is d = 0.282 nm. A
monochromatic beam of X-rays produces a Bragg maximum when its glancing angle
with these planes is = 7o . Assuming that this is a first order m

Brownian Motion
In 1828 Robert Brown, investigating pollen in water through
a microscope, observed particles moving irregularly.
2 micron spheres
in water
2 micron spheres
in goo (DNA solution)
(Movies from Eric Weeks)
Theories of Brownian Motion
Wrong t

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
19) A
simple harmonic oscillator has an amplitude of 3.50 cm and a maximum speed of
26.0 cm/s. What is its speed when the displacement is 1.75 cm?
A) 12.0 cm/s
B) 15.

12) A
95 N force exerted at the end of a 0.50 m long torque wrench gives rise to a torque of
15 N m. What is the angle (assumed to be less than 90) between the wrench handle
and the direction of the applied force?
A) 25
B) 22
C) 18
D) 14
12)
Answer: C
lig

flows in the horizontal pipe shown in the figure. At point A the area is 25.0 cm2
and the speed of the water is 2.00 m/s. At B the area is 16.0 cm2. The fluid in the
manometer is mercury, which has a density of 13,600 kg/m3. We can treat water as an
ideal

sealed 26-m3 tank is filled with 2000 moles of oxygen gas (O2) at an initial
temperature of 270 K. The gas is heated to a final temperature of 460 K. The ATOMIC
mass of oxygen is 16.0 g/mol, and the ideal gas constant is R = 8.314 J/mol K =
0.0821 L atm/m