Download PHYS 203 General Physics

PHYS 203 General Physics
Final Exam Review Sheet
The final exam is Monday, June 7, at 1:00 pm. The exam will be comprehensive. It will
be closed book. All necessary equations will be provided, but you may bring a 3 × 5 card
with equations written on it if you wish. You are also responsible for George Gamow’s book,
Chapters 1 through 6.
Look over the Mid-term Review Sheets for other study problems. Following are some
problems from previous final exams. Also, there is a sample final exam available on the class
web site. Finally, Review your labs.
1. (This was on the Midterm 2 review sheet also.) Things to memorize: (1) the
wavelength ranges for IR, visible, and UV light, in nm; (2) the approximate size of an
atom; (3) the approximate size of a nucleus; (4) the approximate size of a bacterium;
(5) the approximate size of a human hair; (6) the velocity of light; and (7) the accepted
age of the universe.
2. Suppose you shine light through a diffraction grating in which the grooves (or scratches)
are 4.00 µm apart. You observe a 3rd-order maximum at an angle of 25◦ from the
central maximum. (A) What is the wavelength of the light? (B) Suppose you repeat
the experiment under water. At what angle would you see the 3rd-order maximum
now?
3. Suppose a laser beam is directed onto the flat surface of a piece of transparent plastic,
and an angle 70◦ from the normal. The angle of refraction (when the beam enters the
material) is measured to be 36.0◦ . What is the index of refraction of the plastic?
4. Planck presented his Blackbody Formula, which introduced the idea of the quantum
of energy, in 1900. About how long was it before quantum theory matured into a more
or less complete theory? Why did it take this long? (Gamow has something to say
about this.)
5. What is the Heisenberg Uncertainty Principle? What is there about it that Einstein
did not like?
6. Know the contributions of each of the following to our understanding of the structure of
the atom, or to our understanding of matter in general: Planck, de Broglie, Rutherford,
Bohr, Einstein, and Dirac.
7. Early models of the atom assumed a large “soft” ball of positive charge with electrons
embedded in it. What evidence do we have that this is wrong?
8. The mass energy of an electron is 0.511 MeV. What is the speed of an electron whose
total energy is three times that, or 1.53 MeV?
9. Suppose that Planck’s constant h were to change from 6.6×10−34 J-s to 0.066 J-s.
What kind of effects might you notice from this change?
10. The microwaves we used in the lab had wavelengths of about 3.2 cm. What is the
energy of a photon with this wavelength?
11. A doubly-ionized Lithium atom has only a single electron, so the Bohr model can
describe it. The red Balmer line from hydrogen is due to a n = 3 −→ n = 2 transition.
What transition in doubly-ionized lithium will result in the same wavelength of emitted
light?
12. The tracks of a CD (compact disk) are 1.60 µm apart. When laser light of a certain
wavelength is shined onto a CD in a direction normal to the surface, a second-order
interference maximum is observed at 34◦ from the normal. Find the wavelength of the
laser light.
13. Police radar guns often use microwaves of frequency 24.2 GHz. What is the wavelength of these microwaves? What is the energy, in eV, of a microwave photon at this
frequency?
14. Which of the physicists described in Gamow’s book was a duke? Who was Nicholas
Baker? Who invented a wave equation which predicted 3-dimensional “standing waves”
of electrons in atoms? Who invented the Uncertainty Principle? Which two physicists
had a long-running debate over the “probabilistic” interpretation of quantum mechanics? Who predicted the existence of anti-matter?
15. Write down the nuclear reaction equation for
228
90 Th
undergoing α-decay.
−
22
16. Write down the equation for 24
11 Na undergoing β -decay (beta decay.) How about 11 Na
undergoing β + -decay (positron emission)?
17. Suppose a hydrogen atom is excited by an electrical discharge and ends up in a state
n = 7. It decays to n = 6 with emission of a photon.
(A) What is the energy of this photon, in eV?
(B) What is the wavelength of the photon? In what region of the spectrum is this?
18. A certain computer monitor (the old kind) accelerates electrons through a voltage of
3000 V: there is a 3000-V potential between the electron source and the screen.
(A) Find the de Broglie wavelength of the electrons just before they hit the screen.
(Note: you should first decide whether or not to use relativity, or just use the classical
expression for kinetic energy.)
(B) Find the minimum wavelength of x-rays that are emitted from the screen as a
result of the electrons colliding with it.
19. Suppose an electron is send toward a small slit in a piece of metal, in vacuum.
The slit is 2.0 µm wide. If the electron is headed
in the “y” direction, we could call the plane of the
slit the “x” direction. By localizing the electron in
the x-direction, we introduced uncertainty in its
momentum in that direction. We know the electron’s position, with an uncertainty ∆x ≈ ±1µm.
1 µm
Use the Uncertainty Principle to estimate the un= half width
certainty in its momentum along the x-direction.
Then find the uncertainty in its velocity in the
x-direction. (This is why the electrons diffract
(spread out) and form a fuzzy diffraction pattern
on a detector.)
20.
45
20 Ca
is an isotope sometimes used in biochemistry. It decays by β − -decay, and its
half-life is 164 days. (A) Find the decay constant λ of calcium-45.
(B) If my sample of calcium-45 has an activity of 1000 Bq when it is produced, what
will its activity be 1 year later?
(C) Write down the nuclear reaction for the β-decay of
45
20 Ca.
Answers to selected questions.
#2 λ = 563 nm; θ = 18.5◦ .
#3 n = 1.60
#8 √ 1 2 2 = 3, so v = 0.942c
1−v /c
#10 3.4×10−5 eV
#12 λ = 447 nm
#17. E = 0.1002 eV; λ =12.37 µm: infrared.
#18. (A) λ = 0.022 nm, (B) λmin =0.41 nm
#19. ∆x ∆p ∼
h
4π
so
hc
= 98.7 eV-nm
4π
98.7 eV-nm
≈ 0.1 eV
∆(pc) ∼
1000 nm
∆x ∆(pc) ∼
Then ∆p works out to about 5×10−29 kg m/s. This small number shouldn’t surprise
use since it is in SI units. The uncertainty in velocity is then (∆p)/m:
∆v =
∆p
∆(pc)
0.1 eV
=
c=
(3×108 m/s) = 60 m/s
2
m
mc
5×105 eV