Introduction to SAT II Physics - FreeExamPapers

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Because the electron can only make certain jumps in its energy level, it can only emit photons of certain frequencies. Because it makes these jumps, and does not emit a steady flow of energy, the electron will never spiral into the proton, as Rutherford’s model suggests. Also, because an atom can only emit photons of certain frequencies, a spectroscopic image of the light emanating from a particular element will only carry the frequencies of photon that element can emit. For instance, the sun is mostly made of hydrogen, so most of the light we see coming from the sun is in one of the allowed frequencies for energy jumps in hydrogen atoms. Analogies with the Planetary Model Because the electron of a hydrogen atom orbits the proton, there are some analogies between the nature of this orbit and the nature of planetary orbits. The first is that the centripetal force in both cases is . That means that the centripetal force on the electron is directly proportional to its mass and to the square of its orbital velocity and is inversely proportional to the radius of its orbit. The second is that this centripetal force is related to the electric force in the same way that the centripetal force on planets is related to the gravitational force: where e is the electric charge of the electron, and Ze is the electric charge of the nucleus. Z is a variable for the number of protons in the nucleus, so in the hydrogen atom, Z = 1. The third analogy is that of potential energy. If we recall, the gravitational potential energy of a body in orbit is . Analogously, the potential energy of an electron in orbit is: Differences from the Planetary Model However, the planetary model places no restriction on the radius at which planets may orbit the sun. One of Bohr’s fundamental insights was that the angular momentum of the electron, L, must be an integer multiple of . The constant is so common in quantum physics that it has its own symbol, . If we take n to be an integer, we get: Consequently, . By equating the formula for centripetal force and the formula for electric force, we can now solve for r: 330
Don’t worry: you don’t need to memorize this equation. What’s worth noting for the purposes of SAT II Physics is that there are certain constant values for r, for different integer values of n. Note also that r is proportional to , so that each successive radius is farther from the nucleus than the one before. Electron Potential Energy The importance of the complicated equation above for the radius of an orbiting electron is that, when we know the radius of an electron, we can calculate its potential energy. Remember that the potential energy of an electron is . If you plug in the above values for r, you’ll find that the energy of an electron in a hydrogen atom at its ground state (where n = 1 and Z = 1) is –13.6 eV. This is a negative number because we’re dealing with potential energy: this is the amount of energy it would take to free the electron from its orbit. When the electron jumps from its ground state to a higher energy level, it jumps by multiples of n. The potential energy of an electron in a hydrogen atom for any value of n is: 331
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SATII PHYSICS (FROM SPARKNOTES.COM)
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The Good • Because SAT II Subject
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Which SAT II Subject Tests to Take
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After grumbling, however, you still
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Waves 15-19% 11-15 Waves 10% 7-8 Op
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negative, so E, and not A, is the c
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including them anyway because it’
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Two positively charged particles, o
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will a visual representation reliev
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Physics Hint 6: Be Flexible Knowing
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There are a number of ways to label
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Adding Parallel Vectors If the vect
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The result of multiplying A by c is
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neither parallel nor perpendicular.
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Suppose the hands on a clock are ve
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Vector Addition Practice Questions
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2. A The vector 2A has a magnitude
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path, Alan has traveled a much grea
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school student called Andrea. Andre
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centimeters to the left of its star
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We can learn two things about the a
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Acceleration vs. Time Graphs After
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The variable represents the object
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Note that there are certain conveni
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1. . An athlete runs four laps of a
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10. . A woman runs 40 m to the nort
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We know the total distance the spri
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Principles of Natural Philosophy. I
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The component form of Newton’s Se
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e in the direction. And since the s
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which reflects its resistance to be
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In the diagram above, the weight an
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A student pushes a box that weighs
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1. . Each of the figures below show
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7. . In the figure above, a person
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Since the block is motionless, the
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When we are told that a person push
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EXAMPLE A water balloon of mass m i
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The graph above plots the force exe
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Though energy is always measured in
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there is a negative amount of work
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smallest. The answer to question 3
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Mechanical Energy Average Power Ins
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to a height of 8 m over a time of 4
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8. C When the book reaches the pers
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determining what those right number
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the ground. The system is initially
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calculators, you almost certainly w
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and minimize M.” With such a ques
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2. WHAT IS THE ACCELERATION OF THE
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Adding these two equations together
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force of friction: . Using Newton
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m, placed on a frictionless surface
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Frequency is given in units of cycl
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of the spring due to the gravitatio
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The oscillation of a pendulum is mu
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Velocity Calculating the velocity o
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Practice Questions 1. . Two masses,
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7. . An object of mass 3 kg is atta
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Since the system is in equilibrium,
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velocity, v. Linear momentum is den
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Conservation of Momentum If we comb
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As we might expect, the final veloc
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A pool player hits the eight ball,
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two-dimensional collision is effect
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For a System of Two Particles For a
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At the front end of the boat, the f
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4. . A scattering experiment is don
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1. B The athlete imparts a certain
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7. E Momentum is conserved in this
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The diver’s translational motion
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30 π/6 45 π/4 60 π/3 90 π/2 180
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elative position to one another. As
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acceleration given its angular velo
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To find the direction of a rigid bo
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A student exerts a force of 50 N on
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The torque that produces the angula
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The masses in the figure above are
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an object sliding down a frictionle
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Velocity Average Angular Accelerati
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3. . What is the direction of the a
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1. D An object that experiences 120
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At the top of the incline, the disk
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from a Latin word meaning “center
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Newton’s Law of Universal Gravita
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when you are beneath the surface of
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EXAMPLE A satellite of mass is laun
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Kepler’s Laws After poring over t
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Practice Questions Questions 1-3 re
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8. . A satellite orbits the Earth a
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Circumference and radius are relate
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learn how heat is transferred from
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heat, like rubber, have a high spec
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Just as specific heat tells us how
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Conduction is the transfer of heat
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Effectively, this equation tells us
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the way that it does. The Laws of T
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There are a number of equivalent fo
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If we know our formulas, this probl
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5. . An ideal gas is enclosed in a
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Asphalt, like most materials, has a
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The things we call atoms today are
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If they come up on SAT II Physics,
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will move in the opposite direction
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Work The work done to move a charge
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Much like gravitational potential e
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3. . A particle of charge +2q exert
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7. . A particle of charge +q is a d
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The vector sum of the three vectors
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Voltage The batteries we use in fla
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This equation tells us that we can
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If the two variables you know are a
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However, each resistor causes a vol
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So = 4 . WHAT IS THE CURRENT RUNNIN
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Consider again the circuit whose to
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This circuit consists of resistors
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The junction rule deals with “jun
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across the loop. We can express the
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capacitance is halved. The proporti
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The Greek letter is called the diel
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4. . Two resistors, and , are ident
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10. . A dielectric is inserted into
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The equivalent capacitance of two c
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The Earth itself acts like a huge b
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Because the velocity vector and the
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A particle with a positive charge o
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The constant is called the permeabi
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1. . The pointer on a compass is th
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7. . A positively charged particle
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1. B To solve this problem, it is h
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If the particle is to move at a con
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flowing in the counterclockwise dir
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Next, let’s calculate the flux th
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Remember that field lines come out
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Magnetic Flux Faraday’s Law / Len
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5. . A wire carrying 5.0 V is appli
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In this equation, A is the amplitud
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Ernst attaches a stretched string t
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A string is tied to a pole at one e
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Page 303 and 304: Because is a positive number, we kn
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Page 365 and 366: Refracted ray Refraction Restoring
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Page 369 and 370: Weber Weight The force involved in
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