Consider a particle moving in a two-dimensional space defined by V = 0 for 0 < x < L and 0 < y < L and V = elsewhere. (a) Write down the wave functions for the particle in this well. (b) Find the...
Find the energies E 311 , E 222 , and E 321 and construct an energy-level diagram for the three-dimensional cubic well that includes the third, fourth, and fifth excited states. Which of the states...
A particle of mass m is confined to a tube of length L. (a) Use the uncertainty relationship to estimate the smallest possible energy. (b) Assume that the inside of the tube is a force-free region...
A particle with mass m and total energy zero is in a particular region of space where its wave function is (x) = Ce -x2/L 2 . (a) Find the potential energy V(x) versus x and (b) Make a sketch of...
A particle is in an infinite square well of size L. Calculate the ground-state energy if (a) The particle is a proton and L = 0.1 nm, a typical size for a molecule; (b) The particle is a proton and L...
The allowed energies for a particle of mass m in a one-dimensional infinite square well are given by Equation 6-24. Show that a level with n = 0 violates the Heisenberg uncertainty principle. En =...
Show that (x, t) = Ae i(kx - t) satisfies both the time dependent Schrdinger equation and the classical wave equation (Equation 6-1). 2-12 c at 6-1
The nuclei listed below have filled j shells plus or minus one nucleon. (For example, 29 14 Si has the 1d 5/2 shell filled for both neutrons and protons plus one neutron in the 2s 1/2 shell.) Use the...
The repulsive force that results in the hard core of the nucleus might be due to the exchange of a particle, just as the strong attractive force is. Compute the mass of such an exchange particle if...
Compute the energy carried by the neutrino in the electron capture decay of 67 Ga to the ground state of 67 Zn.
Using Figure 11-16, find the parameters A and B in Equation 11-30. Figure 11-16 a decay half-life, s 10:20 1015 1010 105 10 10-5 10-10 4 5 1 7 6 8 a kinetic energy, MeV 9 10% y 10 y 10 y 1y 1 d 1h 1...
The decay constant of 22 Na is 0.266 y -1 . (a) Compute the half-life. (b) What is the activity of a sample containing 1.0 g of 22 Na? (c) What is the activity of the sample after 3.5 years have...
The decay constant of 235 U is 9.8 x 10 -10 y -1 . (a) Compute the half-life. (b) How many decays occur each second in a 1.0 g sample of 235 U? (c) How many 235 U atoms will remain in the 1.0 mg...
39 Ca and 39 K are a mirror pair, 39 Ca decaying into 39 K. Use Equations 11-1 and 11-2 to compute the radius of 40 Ca. U = 319 3 1 q 5 4 R 11-1
Compute the charge distribution radius from Equation 11-5 and the nuclear force radius from Equation 11-7 for the following nuclides: (a) 16 O, (b) 63 Cu, and (c) 208 Pb. R= (1.07 0.02) 4/ fm t=2.4...
The magnetic moment of 14 N is 0.4035 N. Show that this value is not compatible with a model of the nucleus that consists of protons and electrons.
Suppose that the deuteron really did consist of two protons and one electron. (It doesnt!) Compute the spin and magnetic moment of such a deuterons ground state and compare the results with the...
The spin of the ground state of Li, which constitutes 7.5 percent of natural lithium, is zero. Show that this value is not compatible with a model of the nucleus that consists of protons and...
Use dimensional analysis to show that the expression for the energy levels of hydrogenlike atoms given by Equation 7-25 has the units of energy. 22 kZe E. - (46) +- 2 2n n 7-25
At what values of r/a 0 is the radial function R 30 equal to zero? (See Table 7-2.) Table 7-2 n=1 n=2 n=3 Table 7-2 Radial functions for hydrogen l=0 e = 0 l=1 l = 0 l = 1 l = 2 R10 R0 R1 R31 = R32 =...
Compute the wavelength and frequency of the series limit for the Lyman, Balmer, and Paschen spectral series of hydrogen.
The force on a magnetic moment with z component z moving in an inhomogeneous magnetic field is given by Equation 7-51. If the silver atoms in the Stern- Gerlach experiment traveled horizontally 1 m...
FIGURE Q2.14 shows the velocity-versus-time graph for a moving object. At which lettered point or points: a. Is the object speeding up? b. Is the object slowing down? c. Is the object moving to the...
Is the particle in FIGURE Q1.3 speeding up? Slowing down? Or can you tell? Explain. Figure Q1.3 ..
Does the object represented in FIGURE Q1.5 have a positive or negative value of α y ? Explain. Figure Q1.5
Determine the signs (positive, negative, or zero) of the position, velocity, and acceleration for the particle in FIGURE Q1.6. Figure Q1.6
Determine the signs (positive, negative, or zero) of the position, velocity, and acceleration for the particle in FIGURE Q1.7. Figure Q1.7 0-
FIGURE EX1.9 shows five points of a motion diagram. Use Tactics Box 1.3 to find the average acceleration vectors at points 1, 2, and 3. Draw the completed motion diagram showing velocity vectors and...
A goose flies toward a pond. It lands on the water and slides for some distance before it comes to a stop. Draw the motion diagram of the goose, starting shortly before it hits the water and assuming...
You use a long rubber band to launch a paper wad straight up. Draw a complete motion diagram of the paper wad from the moment you release the stretched rubber band until the paper wad reaches its...
A roof tile falls straight down from a two-story building. It lands in a swimming pool and settles gently to the bottom. Draw a complete motion diagram of the tile?
Write a short description of the motion of a real object for which FIGURE EX1.19 would be a realistic position-versus-time graph. Figure EX 1.19 x (m) 300 200 100 - 1 (s) 600 200 400
Write a short description of the motion of a real object for which FIGURE EX1.20 would be a realistic position-versus-time graph. Figure EX 1.20 x (mi) 120- 80- 40- (h) 3 4 5 2
Draw a pictorial representation for the following problem. Do not solve the problem. The light turns green, and a bicyclist starts forward with an acceleration of 1.5 m/s 2 . How far must she travel...
Convert the following to SI units: a. 75 in b. 3.45 10 6 yr c. 62 ft/day d. 2.2 10 4 mi 2
Using the approximate conversion factors in Table 1.5, convert the following SI units to English units without using your calculator. Table 1.5 1 cm 1/2 in 10 cm 4 in 1 m 1 yard 1 m 3 feet 1 km ...
Using the approximate conversion factors in Table 1.5, convert the following to SI units without using your calculator. Table 1.5 1 cm 1/2 in 10 cm 4 in 1 m 1 yard 1 m 3 feet 1 km 0.6 mile 1 m/s...
Compute the following numbers, applying the significant figure rules adopted in this textbook. a. 33.3 25.4 b. 33.3 25.4 c. 33.3 d. 333.3 25.4
Perform the following calculations with the correct number of significant figures. a. 159.31 204.6 b. 5.1125 + 0.67 + 3.2 c. 7.662 - 7.425 d. 16.5/3.45
Estimate (dont measure!) the length of a typical car. Give your answer in both feet and meters. Briefly describe how you arrived at this estimate?
Estimate the height of a telephone pole. Give your answer in both feet and meters. Briefly describe how you arrived at this estimate?
Estimate the average speed with which the hair on your head grows. Give your answer in both m/s and mm/hour. Briefly describe how you arrived at this estimate?
Motor neurons in mammals transmit signals from the brain to skeletal muscles at approximately 25 m/s. Estimate how long in ms it takes a signal to get from your brain to your hand?
A jet plane is cruising at 300 m/s when suddenly the pilot turns the engines up to full throttle. After traveling 4.0 km, the jet is moving with a speed of 400 m/s. What is the jets acceleration as...
You would like to stick a wet spit wad on the ceiling, so you toss it straight up with a speed of 10 m/s. How long does it take to reach the ceiling, 3.0 m above? Draw a complete pictorial...
A speed skater moving across friction less ice at 8.0 m/s hits a 5.0-m-wide patch of rough ice. She slows steadily, then continues on at 6.0 m/s. What is her acceleration on the rough ice? Draw a...
Sam is recklessly driving 60 mph in a 30 mph speed zone when he suddenly sees the police. He steps on the brakes and slows to 30 mph in three seconds, looking nonchalant as he passes the officer. How...
A motorist is traveling at 20 m/s. He is 60 m from a stoplight when he sees it turn yellow. His reaction time, before stepping on the brake, is 0.50 s. What steady deceleration while braking will...
A car traveling at 30 m/s runs out of gas while traveling up a 10 slope. How far up the hill will the car coast before starting to roll back down? Draw a complete pictorial representation. Do not...
Ice hockey star Bruce Blades is 5.0 m from the blue line and gliding toward it at a speed of 4.0 m/s. You are 20 m from the blue line, directly behind Bruce. You want to pass the puck to Bruce. With...
David is driving a steady 30 m/s when he passes Tina, who is sitting in her car at rest. Tina begins to accelerate at a steady 2.0 m/s 2 at the instant when David passes. How far does Tina drive...
Nicole throws a ball straight up. Chad watches the ball from a window 5.0 m above the point where Nicole released it. The ball passes Chad on the way up, and it has a speed of 10 m/s as it passes him...
David is driving a steady 30 m/s when he passes Tina, who is sitting in her car at rest. Tina begins to accelerate at a steady 2.0 m/s 2 at the instant when David passes. a. How far does Tina drive...
A cat is sleeping on the floor in the middle of a 3.0-m-wide room when a barking dog enters with a speed of 1.50 m/s. As the dog enters, the cat (as only cats can do) immediately accelerates at 0.85...
Water drops fall from the edge of a roof at a steady rate. A fifth drop starts to fall just as the first drop hits the ground. At this instant, the second and third drops are exactly at the bottom...
A rock is thrown from a bridge at an angle 30 below horizontal. Immediately after the rock is released, is the magnitude of its acceleration greater than, less than, or equal to g? Explain.
An electromagnet on the ceiling of an airplane holds a steel ball. When a button is pushed, the magnet releases the ball. The experiment is first done while the plane is parked on the ground, and the...
Santa loses his footing and slides down a frictionless, snowy roof that is tilted at an angle of 30. If Santa slides 10 m before reaching the edge, what is his speed as he leaves the roof?
A car skids to a halt to avoid hitting an object in the road. Draw a basic motion diagram, using the images from the video, from the time the skid begins until the car is stopped?
A rocket is launched straight up. Draw a basic motion diagram, using the images from the video, from the moment of liftoff until the rocket is at an altitude of 500 m?
a. Write a paragraph describing the particle model. What is it, and why is it important? b. Give two examples of situations, different from those described in the text, for which the particle model...
You drop a soccer ball from your third-story balcony. Use the particle model to draw a motion diagram showing the balls position and average velocity vectors from the time you release the ball until...
A softball player slides into second base. Use the particle model to draw a motion diagram showing his position and his average velocity vectors from the time he begins to slide until he reaches the...
a. FIGURE EX1.8 shows the first three points of a motion diagram. Is the objects average speed between points 1 and 2 greater than, less than, or equal to its average speed between points 0 and 1?...
FIGURE EX1.10 shows two dots of a motion diagram and vector 1 Copy this figure, then add dot 3 and the next velocity vector 2 if the acceleration vector at dot 2 (a) Points up and (b) Points down....
Show a partial motion diagram. For each: a. Complete the motion diagram by adding acceleration vectors. b. Write a physics problem for which this is the correct motion diagram. Be imaginative! Dont...
A regulation soccer field for international play is a rectangle with a length between 100 m and 110 m and a width between 64 m and 75 m. What are the smallest and largest areas that the field could...
As an architect, you are designing a new house. A window has a height between 140 cm and 150 cm and a width between 74 cm and 70 cm. What are the smallest and largest areas that the window could be?
A 5.4-cm-diameter cylinder has a length of 12.5 cm. What is the cylinders volume in SI units?
An intravenous saline drip has 9.0 g of sodium chloride per liter of water. By definition, 1 mL = 1 cm 3 . Express the salt concentration in kg/m 3 ?
The quantity called mass density is the mass per unit volume of a substance. What are the mass densities in SI units of the following objects? a. A 215 cm 3 solid with a mass of 0.0179 kg. b. 95 cm 3...
FIGURE Q2.4 shows a position-versus-time graph for the motion of objects A and B as they move along the same axis. a. At the instant t = 1 s, is the speed of A greater than, less than, or equal to...
Figure P1.58 shows a motion diagram of a car traveling down a street. The camera took one frame every 10 s. A distance scale is provided. Figure P1-58 a. Measure the x-value of the car at each dot....
For Questions 1 through 3, interpret the position graph given in each figure by writing a very short story of what is happening. Be creative! Have characters and situations! Simply saying that a car...
FIGURE Q2.5 shows a position-versus-time graph for the motion of objects A and B as they move along the same axis. a. At the instant t = 1 s, is the speed of A greater than, less than, or equal to...
FIGURE Q2.6 shows the position-versus-time graph for a moving object. At which lettered point or points: a. Is the object moving the slowest? b. Is the object moving the fastest? c. Is the object at...
FIGURE Q2.7 shows the position-versus-time graph for a moving object. At which lettered point or points: (a) Is the object moving the fastest? (b) Is the object moving to the left? (c) Is the object...
FIGURE Q2.8 shows six frames from the motion diagrams of two moving cars, A and B. (a) Do the two cars ever have the same position at one instant of time? If so, in which frame number (or numbers)?...
Youre driving along the highway at a steady speed of 60 mph when another driver decides to pass you. At the moment when the front of his car is exactly even with the front of your car, and you turn...
A bicycle is traveling east. Can its acceleration vector ever point west? Explain.
A ball is thrown straight up into the air. At each of the following instants, is the magnitude of the balls acceleration greater than g, equal to g, less than g, or 0? Explain. a. Just after leaving...
A rock is thrown (not dropped) straight down from a bridge into the river below. At each of the following instants, is the magnitude of the rocks acceleration greater than g, equal to g, less than g,...
FIGURE EX2.7 is a somewhat idealized graph of the velocity of blood in the ascending aorta during one beat of the heart. Approximately how far, in cm, does the blood move during one beat? Figure Ex...
FIGURE EX2.8 shows the velocity graph for a particle having initial position x 0 = 0 m at t 0 = 0 s. At what time or times is the particle found at x = 35 m? Figure Ex 2.8 V (m/s) 10- 5. 0- 2 4 6 -t...
a. What constant acceleration, in SI units, must a car have to go from zero to 60 mph in 10 s? b. How far has the car traveled when it reaches 60 mph? Give your answer both in SI units and in feet.
A jet plane is cruising at 300 m/s when suddenly the pilot turns the engines up to full throttle. After traveling 4.0 km, the jet is moving with a speed of 400 m/s. What is the jets acceleration,...
FIGURE EX2.11 shows the velocity graph of a particle moving along the x-axis. Its initial position is x 0 = 2.0 m at t 0 = 0 s. At t = 2.0 s, what are the particles (a) Position, (b) Velocity, and...
FIGURE EX2.12 shows the velocity-versus-time graph for a particle moving along the x-axis. Its initial position is x 0 = 2.0 m at t 0 = 0 s. a. What are the particles position, velocity, and...
a. How many days will it take a spaceship to accelerate to the speed of light (3.0 10 8 m/s) with the acceleration g? b. How far will it travel during this interval? c. What fraction of a light year...
When you sneeze, the air in your lungs accelerates from rest to 150 km/h in approximately 0.50 s. What is the acceleration of the air in m/s 2 ?
A speed skater moving to the left across friction less ice at 8.0 m/s hits a 5.0-m-wide patch of rough ice. She slows steadily, then continues on at 6.0 m/s. What is her acceleration on the rough ice?
A Porsche challenges a Honda to a 400 m race. Because the Porsches acceleration of 3.5 m/s 2 is larger than the Hondas 3.0 m/s 2 , the Honda gets a 1.0 s head start. Who wins? By how many seconds?
A rock is tossed straight up from ground level with a speed of 20 m/s. When it returns, it falls into a hole 10 m deep. (a) What is the rocks velocity as it hits the bottom of the hole? (b) How long...
A snowboarder glides down a 50-m-long, 15 o hill. She then glides horizontally for 10 m before reaching a 25 o upward slope. Assume the snow is friction less. a. What is her velocity at the bottom of...
A small child gives a plastic frog a big push at the bottom of a slippery 2.0-m-long, 1.0-m-high ramp, starting it with a speed of 5.0 m/s. What is the frogs speed as it flies off the top of the ramp?
FIGURE EX2.31 shows the acceleration-versus-time graph of a particle moving along the x-axis. Its initial velocity is v 0x = 8.0 m/s at t 0 = 0 s. What is the particles velocity at t = 4.0 s? Figure...
FIGURE EX2.32 shows the acceleration graph for a particle that starts from rest at t = 0 s. What is the particles velocity at t = 6 s? Figure Ex 2.32 a, (m/s?) 10- 5- 0- -t (s) 2
The position of a particle is given by the function x = (2t 3 - 9t 2 + 12) m, where t is in s. a. At what time or times is v x = 0 m/s? b. What are the particles position and its acceleration at this...
The position of a particle is given by the function x = (2t 3 6t 2 + 12) m, where t is in s. a. At what time does the particle reach its minimum velocity? What is (v x ) min ? b. At what time is the...
Particles A, B, and C move along the x-axis. Particle C has an initial velocity of 10 m/s. In FIGURE P2.37, the graph for A is a position-versus-time graph; the graph for B is a velocity-versus time...