Practice for Test 3, No 1.
1. Which of the following are NOT predicted by the Rutherford model of the atom? (a) The Balmer series. (b) The udeflected passage of alpha particles through gold foil. (c) The decay of the electron into the nucleus by the emission of electromagnetic radiation. (d) All of the Above. (e) None ofh te above.
2. When an electron is accelerated to a higher speed, there will be a decrease in its (a) energy, (b) frequency. (c) wavelength. (d) momentum. (e) All of the above.
3. The quantization of energy E = nhf, is not important for an ordinary pendulum because (a) the formula applies only to mass-spring oscillators. (b) the allowed energies are too closely spaced (because n will be so large). (c) the allowed energies are too widely spaced (because n will be so small). (d) the formula applies only to atoms. (e) the value of h for a pendulaum is too large.
4. Let the charge on the nucleus of a "Borh model" atom be Ze. The energy of the nth state is proportional to (a) Z. (b) Z^2. (c) Z^3. (d) Z^4. (e) Z^5.
5. The Pauli exclusion principle states that (a) none of your relatives named "Pauli" are allowed to come over to your house. (b) people with large feet are not allowed to dine at the E. Fermi Dinner Club in Modena, Italy. (c) no two electrons in orbit around a nucleus can have the same set of quantum numbers. (d) electrons are excluded from being in the nucleus. (e) protons are excluded from the orbital levels of an atom.
6. In a typical nuclear reaction which releases energy, (a) most of the mass is converted into shoe polish. (b) very little of the mass of the constituents is converted into energy. (c) none of hte mass of the constituents is converted into energy. (d) most of the mass of the constituents is converted in to energy. (e) about half of the mass of the constituents is converted into energy.
7. A person moves past you in the "forward" direction (in this case, we will define forward to be from your right to your left). You would notice that the person will be aging slow compared to you. If the person then reverses direction and moves backwards, the person will be (a) Michael Jackson. (b) traveling faster than the speed of light. (c) now aging atthe same rate as you. (d) still aging slower than you. (e) aging faster than you.
8. Suppose that you could travel at speeds approaching the speed of light. What would you observe about yourself? (a) Some of your dimensions have grown smaller. (b) Some of your dimensions have grown larger. (c) Your pulse rate has increased. (d) Your pulse rate has decreased. (e) None of the above.
9. An atom emits a photon when on of its electrons (a) collides with another one of its electrons. (b) undergoes a transition to a state of lower energy. (c) undergoes a transition to a state of higher energy. (d) loses its charge. (e) None of the above is true.
10. What is the ionization energy for the hydrogen atom in its ground state? (a) -13.6 eV. (b) -1.6 eV. (c) 1.6 eV. (d) 13.6 eV. (e) More information must be given (such as the value of the quantum number in the process).
11. If a neutron were to get over 5 x 10-15 m from the center of a nucleus, it would suddenly begin to act as a free particle. This is a demonstration of (a) the small mass of the neutron. (b) the fact that a neutron has a mass about equal to that of the proton. (c) the fact that the magnetic moment of the neutron is zero. (d) the short range nature of the strong interaction. (e) the long range nature of the strong interaction.
12. The reaction A Z X goes to A Z X + photon is a demonstration of (a) Alfa emission. (b) Beta emission. (c) Gamma emission. (d) Photo emission. (e) Orbital emission.
13. A person standing on the ground observing a rocket ship moving past at a speed near c would find the ship to be (a) the same length as when it was at rest. (b) shorter than it was at rest. (c) longer than when it is at rest. (d) shorter when it is approaching him and longer when it is going away. (e) longer when it is approaching him and shorter when it is going away.
14. Balmers original formula depicting the wavelength of observed spectral lines for hydrogen was formulated (a) as a demonstration of Thompson's atomic theory. (b) as a demonstration of Rutherford's atomic theory. (c) as a demonstration of Bohr's atomic theory. (d) to fit experimental information. (e) because Balmer had nothing else to do that day.
15. Bohr model of the atom suggests that the electron in hydrogen can occupy (a) orbits of any radius. (b) only a certain set of orbits with definite radii. (c) only orbits where the electron couldn't jump from one to the next. (d) only orbits where the electron couldn't move at all. (e) None of the above.
16. A particle of rest mass mo moves with a speed 0.6c. Its kinetic energy is (a) 0.18 moc^2. (b) 0.22moc^2. (c) 0.25moc^2. (d) moc^2. (e) 1.25moc^2.
17. A cannonball is inside of a cannon of length 1 m. The mass of the cannonball is 100 Kg. Using h/2pi = 1 x 10E-34 J-sec, what is the minimum uncertainty in the speed of the cannonball? (a) 0.0 m/sec. (b) 1 x 10E-36 m/sec. (c) 1 x 10E-32 m/sec. (d) 3 x 10E8 m/sec. (e) All of the above.
18. A sample of radioactive material has no nuclei, and after a time t, the number remaining nuclei is n. Take the half-life to be 1 sec. After 10 seconds, the ratio n/no will be (recall that ln (.5) = -.693) (a) eE-10. (b) eE-1. (c) eE-69.3. (d) eE-6.93. (e) eE-(3x10E8).
19. Assuming that the average household burns 5 100 W bulbs an average of 5 hours per day 365 days per year, the average energy consumption is about 3.0 x 109 J. How many households could run their lights for en entire year from a 1 gram paper clip, if the paperclip could be converted completely to energy? (a) about 30. (b) about 300. (c) about 3000. (d) about 30000. (e) about 300000.
20. A cannonball of mass 45 kg is carried on a railraod car, which moves past a stationary observer with a speed .999 c. What is the mass of the cannonball as measured by a person in the railroad car? (a) 1006 kg. (b) 542 kg. (c) 45 kg. (d) 2 kg. (e) 0 kg.
21. An astronomer observing a satellite (known to be spherical) moving by the earth, finds that the diameter measured along the direction of motion is 1.0 meters, and the diameter measured perpendicular to the direction of motion is 2.0 meters. (a) What is the speed of the satelitte? (b) How much time does the astronomer say has passed when he sees that 30 sec have passed on the clock in the satellite? (c) If the satellite were to fire a projectile in the direction of its motion with a speed of 0.25c relative to the satellite, with what speed would the stronomer see this projectile moving? Leave your expression as a numerical expression if you wish.
22. A whole bunch of atomic stuff!!!!!! Don't forget angular momentum = mvr, and in this rough caluclation, assume that h/2pi = 1 x 10E-34 J-sec. (a) List the quantum numbers for all of the electrons in the element Neon (Z= 10). Do not forget about spin. (b) A 200 Kg satellite at a height of 100 km above the earth's surface has an orbital speed of 5000 m/sec. Assuming that the results of the Schrodinger equation for hydrogen can be applied to the satellite in orbit, what is the value of the quantum number associated with the orbital angular momentum of the satellite? you can write out an expression, you don't have to solve for the quantum number. (c) Assuming that the results of the Bohr model for hydrogen can be applied to the satellite in orbit, what is the value of the quantum number associated with the orbital angular momentum of the satellite? Get a final value for this one. (d) How is the correspondence principle reflected in your answers to parts (b) and (c)?
Answer Key: 1.A 2.C 3.B 4.B 5.C 6.B 7.D 8.E 9.B 10.D 11.D 12.C 13.B 14.D 15.B 16.C 17.B 18.D 19.D 20.C
Practice for Test 3, No. 2
1. A particle of mass m moves at a speed .6 c. A stationary observer measures that the mass of the object is (a) .8m (b) m. (c) 1.07m. (d) 1.25m. (e) None of the above.
2. A photon in light beam A has twice the energy of one in a light beam B. The ratio of the wavelength of A over the wavelength of B is (a) 1/2. (b) 1/4. (c) 1. (d) 2. (e) 4.
3. According to the Bohr model of the atom, the total number of electron states up to and including n = 3 for a hydrogen atom is (assume that the exclusion and the energy minimum principles are valid) (a) 3. (b) 6. (c) 10. (d) 16. (e) 28.
4. A rectangular clock, of dimensions 20 cm i,30 cm j,and 40 cm k is placed in a moving rocket travelling at .95 c i. The mass of the clock is 50 kg. A stationary observer watching the clock go by sees (a) a clock of mass greater than 50 kg, smaller in all of its spatial dimensions, which runs slow. (b) a clock of mass less than 50 kg, smaller in all of its spatial dimensions, which runs slow. (c) a clock of mass greater than 50 kg, smaller in all of its spatial dimensions, which runs fast. (d) a clock of mass less than 50 kg, smaller in all of its spatial dimensions, which runs fast. (e) None of the above.
5. Which of the following constitutes a non-inertial reference frame relative to the earth? (a) A car moving at constant velocity. (b) A block sliding down an incline (with friction) at constant velocity. (c) A railroad car moving with constant momentum along a track. (d) A car going around a corner at constant speed. (e) None of the above.
6. A boy stays on the earth while his identical twin sister leaves in a rocket ship traveling at a speed near the speed of light. Each person has a heart rate of 70 beats/min when standing on the earth. The boy on the earth looks through the window of the rocket and notices that his sister in the rocket has a heart rate of 25 beats/min, while his rate is 70 beats/min. The girl on the rocket records her heart rate to be 70 beats/min, and if she looks out the window back at the earth, her brothers heart rate will be (in beats/min) (a) greater than 70. (b) 70. (c) between 70 and 25. (d) 25. (e) less than 25.
7. According to Einstein's theory of special relativity (a) space and time are aspects of each other. (b) mass and energy are aspects of each other. (c) space and mass are aspects of each other. (d) Both (a) and (b). (e) Both (b) and (c).
8. The various emission spectral series (Lyman, Balmer, etc) are a result of (a) An electron falling from a higher Bohr orbit to a lower Bohr orbit. (b) An electron falling from a lower Bohr orbit to a higher Bohr orbit. (c) The radiation of a photon from an electron in a given Bohr orbit. (d) Radioactivity. (e) Geometrodynamics.
9. An electron beam is incident upon a single slit, and the results of the passage through the slit is viewed on a fluorescent screen. The fact that a diffraction pattern is seen is a dramatic demonstration of (a) the particle like nature of waves. (b) the wavelike nature of particles. (c) the quantization of electronic states. (d) the Compton effect. (e) All of the above.
10. If you examine the energies of the electrons orbiting a lithium nucleus, you will find that no two electrons will have exactly the same energies. This observation led to the formulation of the (a) Pauli exclusion priciple. (b) Heisenberg uncertainty relation. (c) Bohr energy separation requirement. (d) electronic mutual hatred society. (e) None of the above.
11. An advantage of an electron microscope over an optical microscope is (a) electron microscopes are inexpensive. (b) electron microscopes conserve energy; optical microscopes do not. (c) an electron microscopes resolution is determined by the Rayleigh Criterion; the Rayleigh Criterion plays no role in an optical microscope's resolution. (d) the electrons wavelength in an electron microscope can be made very small as compared with typical wavelengths of visible light. (e) All of the above.
12. It is known that a plot of the mass loss per nucleon has a minimum at Iron. This suggests that iron has (a) the largest number of nucleons allowed by classical theory. (b) the largest number of nucleons allowed by quantum theory. (c) the least binding energy per nucleon. (d) the most binding enegry per nucleon. (e) None of the above.
13. The probability that a particle is in a given small region of space is most closely dependent upon (a) its energy. (b) its momentum. (c) the frequency of its wave function. (d) the wavelength of its wavefunction. (e) the wave amplitude.
14. The quantum number n is most closely associated with what property of the electron in the hydrogen atom? (a) energy. (b) orbital angular momentum. (c) spin angular momentum. (d) magnetic moment. (e) spin angular momentum.
15. No state in an atom can be occupied by more than one electron. This is most closely related to the (a) wave nature of matter. (b) finite value for the speed of light. (c) Bohr magneton. (d) Pauli exclusion principle. (e) the electronic "no en casa" principle.
16. According to the uncertainty principle, the uncertainty in the measurement of the momentum (in Kg-m/sec) of an automobile for which the uncertainty in the position is 1 x 10-4 m is (use h/2 = 1 x 10-34 J-sec) (a) 1.0 x 10-20. (b) 1.0 x 10-30. (c) 4.0 x 10-40. (d) 2.0 x 10-30. (e) 3.0 x 10-20.
17. The work function of a certain material is 1.00 eV. What is the longest possible wavelength of incident light which will produce photoelectrons (that is, electrons with zero kinetic energy)? For this rough calculation, take 1 eV = 2 x 10-19 J, and Planck's constant h = 6 x 10-34 j-sec.. (a) 100 nm. (b) 450 nm. (c) 900 nm. (d) 1800 nm. (e) 7500 nm.
18. An hypothetical atom has three energy levels, where the energy of the first shell is 3 Joules, the energy of the second shell is 7 Joules, and the energy of the third shell is 12 Joules. If electron "falls" from the second to the first shell, what is the energy of the emitted photon? (a) 3 Joules. (b) 4 Joules. (c) 5 Joules. (d) 6 Joules. (e) 7 Joules.
19. A railroad car moves at a speed .6 c. The car has a cannon on it which fires a projectile in the direction of motion of the car. The projectile leaves the barrel of the cannon at a speed .8 c. How fast does the projectile move according to a stationary observer watching the car go by? (a) 1.4 c. (b) c. (c) .946 c. (d) .822 c. (e) .8 c.
20. About how many photons are contained in a .01 sec long laser pulse from a .1 W laser if the laser produces electromagnetic waves of wavelength 550 nm? (a) 10. (b) 10^5. (c) 10^10. (d) 10^15. (e) 10^20.
21. The half-life of N is about 7 sec. What fraction of the original number of atoms will be present after 30 sec?
22. A photon has a wavelength of 663 nm (1 nm = 10-9 m). (a) What is the momentum of the photon?(b) If this photon is incident upon a metallic surface, and as a result electrons are ejected with a kinetic energy of 1 x 10-19 J, what is the work function of the metal? (c) What is the critical wavelength for this metal? (d) Calculate the DeBroglie wavelength for the electron ejected in part (b). You can leave your answer in the form of a numerical expression; no need to multiply it all out.
ANSWERS KEY: 1.D 2.A 3.A 4.E 5.D 6.D 7.D 8.A 9.B 10.A 11.D 12.D 13.E 14.A 15.D 16.B 17.C 18.B 19.C 20.D

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