In the ground state of hydrogen, the uncertainty in the position of the electron is roughly 0.10 nm. If the speed of the electron is approximately the same as the uncertainty in its speed, about how fast is it moving?
> What is the energy of a photon that, when absorbed by a hydrogen atom, could cause an electronic transition from (a) The n = 2 state to the n = 5 state and (b) The n = 4 state to the n = 6 state?
> A soap bubble (n = 1.33) having a wall thickness of 120 nm is floating in air. (a) What is the wavelength of the visible light that is most strongly reflected? (b) Explain how a bubble of different thickness could also strongly reflect light of this same
> Following are four possible transitions for a hydrogen atom (a) Which transition will emit the shortest - wavelength photon? (b) For which transition will the atom gain the most energy? (c) For which transition(s) does the atom lose energy?
> A hydrogen atom emits a photon of wavelength 656 nm. From what energy orbit to what lower - energy orbit did the electron jump?
> A photon is emitted when a hydrogen atom undergoes a transition from the n = 5 state to the n = 3 state. Calculate (a) The wavelength, (b) The frequency, and (c) The energy (in eV) of the emitted photon.
> Show that the speed of the electron in the nth Bohr orbit in hydrogen is given by
> For a hydrogen atom in its ground state, use the Bohr model to compute (a) The orbital speed of the electron, (b) The kinetic energy of the electron, and (c) The electrical potential energy of the atom.
> A hydrogen atom is in its first excited state (n = 2). Using the Bohr theory of the atom, calculate (a) The radius of the orbit, (b) The linear momentum of the electron, (c) The angular momentum of the electron, (d) The kinetic energy, (e) The potential
> What is the (a) Energy in eV and (b) Wavelength in μm of a photon that, when absorbed by a hydrogen atom, could cause a transition from the n = 3 to the n = 6 energy level?
> Singly ionized helium (He+) is a hydrogen - like atom. Determine the energy in eV required to raise a He+ electron from the n = 1 to the n = 2 energy level.
> Determine the energies in eV of the (a) Second and (b) Third energy levels of the hydrogen atom. Calculate the orbital radius in nm of an electron in hydrogen’s (c) Second and (d) Third energy levels.
> The so - called Lyman - α photon is the lowest energy photon in the Lyman series of hydrogen and results from an electron transitioning from the n = 2 to the n = 1 energy level. Determine (a) The energy in eV and (b) The wavelength in nm of a Lyman - α p
> Waves from a radio station have a wavelength of 3.00 x 102 m. They travel by two paths to a home receiver 20.0 km from the transmitter. One path is a direct path, and the second is by reflection from a mountain directly behind the home receiver. What is
> In a Rutherford scattering experiment, an α - particle (charge = +2e) heads directly toward a gold nucleus (charge = +79e). The α - particle had a kinetic energy of 5.0 MeV when very far (r ( ∞) from the nucleus. Assuming the gold nucleus to be fixed in
> The “size” of the atom in Rutherford’s model is about 1.0 x 10-10 m. (a) Determine the speed of an electron moving about the proton using the attractive electrostatic force between an electron and a proton separated by this distance. (b) Does this speed
> An isolated atom of a certain element emits light of wavelength 520. nm when the atom falls from its fifth excited state into its second excited state. The atom emits a photon of wavelength 410. nm when it drops from its sixth excited state into its seco
> Does the light emitted by a neon sign constitute a continuous spectrum or only a few colors? Defend your answer.
> The ionization energies for Li, Na, K, Rb, and Cs are 5.390, 5.138, 4.339, 4.176, and 3.893 eV, respectively. Explain why these values are to be expected in terms of the atomic structures.
> List some ways in which quantum mechanics altered our view of the atom pictured by the Bohr theory.
> Can the electron in the ground state of hydrogen absorb a photon of energy less than 13.6 eV? Can it absorb a photon of energy greater than 13.6 eV? Explain.
> Why are three quantum numbers needed to describe the state of a one - electron atom (ignoring spin)?
> Suppose the electron in the hydrogen atom obeyed classical mechanics rather than quantum mechanics. Why should such a hypothetical atom emit a continuous spectrum rather than the observed line spectrum?
> An energy of about 21 eV is required to excite an electron in a helium atom from the 1s state to the 2s state. The same transition for the He+ ion requires approximately twice as much energy. Explain.
> Monochromatic light of wavelength λ is incident on a pair of slits separated by 2.40 x 10-4 m, and forms an interference pattern on a screen placed 1.80 m away from the slits. The first - order bright fringe is 4.52 mm from the center of the central maxi
> A nonrelativistic electron and a nonrelativistic proton are moving and have the same de Broglie wavelength. Which of the following are also the same for the two particles? (a) Speed (b) Kinetic energy (c) Momentum (d) Frequency
> True or False: As the momentum of a particle of mass m increases, its wavelength increases.
> A photon of energy E0 strikes a free electron, with the scattered photon of energy E moving in the direction opposite that of the incident photon. In this Compton effect interaction, what is the resulting kinetic energy of the electron? (a) E0 (b) E (c)
> An x - ray photon is scattered by an electron. Does the frequency of the scattered photon relative to that of the incident photon (a) Increase, (b) Decrease, or (c) Remain the same?
> True or False: When a photon scatters off an electron, the photon loses energy.
> (a) What is the surface temperature of Betelgeuse, a red giant star in the constellation of Orion, which radiates with a peak wavelength of about 970 nm? (b) Rigel, a bluish - white star in Orion, radiates with a peak wavelength of 145 nm. Find the tempe
> From the scattering of sunlight, J. J. Thomson calculated the classical radius of the electron as having the value 2.82 x 10-15 m. Sunlight with an intensity of 5.00 x 102 W/ m2 falls on a disk with this radius. Assume light is a classical wave and the l
> How fast must an electron be moving if all its kinetic energy is lost to a single x - ray photon (a) At the high end of the x - ray electromagnetic spectrum with a wavelength of 1.00 x 10-8 m and (b) At the low end of the x - ray electromagnetic spectrum
> Red light of wavelength 670. nm produces photoelectrons from a certain photoemissive material. Green light of wavelength 520. nm produces photoelectrons from the same material with 1.50 times the maximum kinetic energy. What is the material’s work functi
> A light source of wavelength λ illuminates a metal and ejects photoelectrons with a maximum kinetic energy of 1.00 eV. A second light source of wavelength λ /2 ejects photoelectrons with a maximum kinetic energy of 4.00 eV. What is the work function of t
> Radio waves from a star, of wavelength 2.50 x 102 m, reach a radio telescope by two separate paths, as shown in Figure P24.13. One is a direct path to the receiver, which is situated on the edge of a cliff by the ocean. The second is by reflection off th
> An electron initially at rest recoils after a head - on collision with a 6.20 - keV photon. Determine the kinetic energy acquired by the electron.
> Photons of wavelength 4.50 x 102 nm are incident on a metal. The most energetic electrons ejected from the metal are bent into a circular arc of radius 20.0 cm by a magnetic field with a magnitude of 2.00 x 10-5 T. What is the work function of the metal?
> Johnny Jumper’s favorite trick is to step out of his 16th - story window and fall 50.0 m into a pool. A news reporter takes a picture of 75.0 - kg Johnny just before he makes a splash, using an exposure time of 5.00 ms. Find (a) Johnny’s de Broglie wavel
> Figure P27.45 shows the spectrum of light emitted by a firefly. (a) Determine the temperature of a blackbody that would emit radiation peaked at the same frequency. (b) Based on your result, explain whether firefly radiation is blackbody radiation. Figu
> An x - ray tube is operated at 5.00 x 104 V. (a) Find the minimum wavelength of the radiation emitted by this tube. (b) If the radiation is directed at a crystal, the first - order maximum in the reflected radiation occurs when the grazing angle is 2.5°.
> A 2.0 - kg object falls from a height of 5.0 m to the ground. If the change in the object’s kinetic energy could be converted to visible light of wavelength 5.0 x 10-7 m, how many photons would be produced?
> Find the speed of an electron having a de Broglie wavelength equal to its Compton wavelength.
> A microwave photon in the x - band region has a wavelength of 3.00 cm. Find (a) The momentum, (b) The frequency, and (c) The energy of the photon in electron volts.
> (a) Show that the kinetic energy of a nonrelativistic particle can be written in terms of its momentum as KE = p2/2m. (b) Use the results of part (a) to find the minimum kinetic energy of a proton confined within a nucleus having a diameter of 1.0 x 10-1
> The average lifetime of a muon is about 2 μs. Estimate the minimum uncertainty in the energy of a muon.
> A student sets up a double - slit experiment using monochromatic light of wavelength λ. The distance between the slits is equal to 25 λ. (a) Find the angles at which the m = 1, 2, and 3 maxima occur on the viewing screen. (b) At what angles do the first
> In a nonrelativistic experiment, an electron and a proton are each located along the x - axis to within an uncertainty of 2.50 μm. Determine the minimum uncertainty in the x - component of the velocity of (a) The electron, and (b) The proton.
> An electron and a 0.0200 - kg bullet each have a velocity of magnitude 5.00 x 102 m/s, accurate to within 0.0100%. Within what lower limit could we determine the position of each object along the direction of the velocity?
> An electron is located on a pinpoint having a diameter of 2.5 μm. What is the minimum uncertainty in the speed of the electron?
> A nonrelativistic particle of mass m and charge q is accelerated from rest through a potential difference ΔV. (a) Use conservation of energy to find a symbolic expression for the momentum of the particle in terms of m, q, and ΔV. (b) Write a symbolic exp
> The resolving power of a microscope is proportional to the wavelength used. A resolution of 1.0 x 10-11 m (0.010 nm) would be required in order to “see” an atom. (a) If electrons were used (electron microscope), what minimum kinetic energy would be requi
> An electron and a 6.00 - kg bowling ball each have 4.50 eV of kinetic energy. Calculate (a) λe and (b) λb, the de Broglie wavelengths of the electron and the bowling ball, respectively. (c) Calculate the wavelength λp of a 4.50 - eV photon.
> De Broglie postulated that the relationship λ = h/p is valid for relativistic particles. What is the de Broglie wavelength for a (relativistic) electron having a kinetic energy of 3.00 MeV?
> Calculate the de Broglie wavelength of a proton moving at (a) 2.00 x 104 m/s and (b) 2.00 x 107 m/s.
> (a) If the wavelength of an electron is 5.00 x 10-7 m, how fast is it moving? (b) If the electron has a speed equal to 1.00 x 107 m/s, what is its wavelength?
> A riverside warehouse has two open doors, as in Figure P24.11. Its interior is lined with a sound - absorbing material. A boat on the river sounds its horn. To person A, the sound is loud and clear. To person B, the sound is barely audible. The principal
> In a Compton scattering experiment, an x - ray photon scatters through an angle of 17.4° from a free electron that is initially at rest. The electron recoils with a speed of 2180 km/s. Calculate (a) The wavelength of the incident photon and (b) The angle
> A 0.110 - nm photon collides with a stationary electron. After the collision, the electron moves forward and the photon recoils backwards. Find (a) The momentum and (b) The kinetic energy of the electron.
> A 25.0 - pm x - ray photon scatters off a free electron at A (Fig. P27.26), producing a photon of wavelength λ' traveling at an angle θ = 40.0° relative to the first photon’s direction. This second p
> A 0.00160 - nm photon scatters from a free electron. For what (photon) scattering angle does the recoiling electron have kinetic energy equal to the energy of the scattered photon?
> X - rays are scattered from a target at an angle of 55.0° with the direction of the incident beam. Find the wavelength shift of the scattered x - rays.
> X - rays of wavelength 0.140 nm are reflected from a certain crystal, and the first - order maximum occurs at an angle of 14.4°. What value does this give for the inter-planar spacing of the crystal?
> The first - order diffraction maximum is observed at 12.6° for a crystal having an inter-planar spacing of 0.240 nm. How many other orders can be observed in the diffraction pattern, and at what angles do they appear? Why is there an upper limit to the n
> Potassium iodide has an inter-planar spacing of d = 0.296 nm. A monochromatic x - ray beam shows a first - order diffraction maximum when the grazing angle is 7.6°. Calculate the x - ray wavelength.
> When x - rays of wavelength of 0.129 nm are incident on the surface of a crystal having a structure similar to that of NaCl, a first - order maximum is observed at 8.15°. Calculate the inter-planar spacing of the crystal based on this information.
> Lead has a prominent x - ray emission line at 75.0 keV. (a) What is the minimum speed of an incident electron that could produce this emission line? (b) What is the wavelength of a 75.0 - keV x - ray photon?
> A pair of parallel slits separated by 2.00 x 10-4 m is illuminated by 633 - nm light and an interference pattern is observed on a screen 2.50 m from the plane of the slits. Calculate the difference in path lengths from each of the slits to the location o
> A laser beam is incident on two slits with a separation of 0.200 mm, and a screen is placed 5.00 m from the slits. If the bright interference fringes on the screen are separated by 1.58 cm, what is the wavelength of the laser light?
> A Million Dollars (a) Estimate the time it would take, in days, to spend $1 million if you spent $1 a second until the $1 million is used up. (b) Calculate the actual time it would take, in days, to spend $1 million if you spent $1 a second. How close wa
> A Dime Look at a dime. Around the edge of a dime are many lines. Estimate the number of lines there are around the edge of a dime.
> Recreational Mathematics
> Find the next three numbers in the sequence. 1, 8, 11, 88, 101, 111, 181, 808, 818, 888, 1001, 1111, ……
> Complete the following square of numbers. Explain how you determined your answer.
> You have purchased one lottery ticket each week for many months and have not won more than $5.00. You decide, based on your past experience, that you are not going to win the grand prize and so you stop playing the lottery. What type of reasoning did you
> While logging on to your computer, you type in your username followed by what you believe is your password. The computer indicates that a mistake has been made and asks you to try again. You retype your username and the same password. Again, the computer
> Estimating Heights If the height of the woman in the photo is 62 in. tall, estimate the height of the tree.
> Interior Angles of a Quadrilateral (a) Construct a quadrilateral (a four-sided figure) and measure the four interior angles with a protractor. What is the sum of the measures? (b) Construct three other quadrilaterals, measure the angles, and record the
> The process of reasoning to a general conclusion through observation of specific cases is called _____________ reasoning.
> Statue of Liberty The length of the torch of the Statue of Liberty, from the tip of the flame to the bottom of the torch’s baton, is 29 feet. Estimate the height of the Statue of Liberty from the top of the base to the top of the torch
> Interior Angles of a Triangle (a) Construct a triangle and measure the three interior angles with a protractor. What is the sum of the measures? (b) Construct three other triangles, measure the angles, and record the sums. Are your answers the same? (c
> The sum of any two odd numbers is divisible by 4.
> The difference of any two counting numbers will be a counting number.
> In Exercises 45 and 46, if each square represents one square unit, estimate the area of the shaded figure in square units.
> The product of any two three-digit numbers is a five-digit number.
> When a counting number is added to 3 and the sum is divided by 2, the quotient will be an even number.
> In Exercises 43 and 44, estimate the percent of area that is shaded in the following figures.
> The sum of any three two-digit numbers is a three-digit number.
> The product of any two counting numbers is divisible by 2.
> 86 + 47.2 + 289.8 + 532.4 + 12.8
> In Exercises 41 and 42, estimate, in degrees, the measure of the angles depicted. For comparison purposes a right angle, /, measures 90°.
> Estimate the number of grapes shown in the photo.
> Pick any number and add 10 to the number. Divide the sum by 5. Multiply the quotient by 5. Subtract 10 from the product. Then subtract your original number. (a) What is the result? (b) Arbitrarily select some different numbers and repeat the process, rec
> Estimate the number of bananas shown in the photo.
> Pick any number and add 1 to it. Find the sum of the new number and the original number. Add 9 to the sum. Divide the new sum by 2 and subtract the original number from the quotient. (a) What is the final number? (b) Arbitrarily select some different num
> Pick any number and multiply the number by 4. Add 6 to the product. Divide the sum by 2 and subtract 3 from the quotient. (a) What is the relationship between the number you started with and the final answer? (b) Arbitrarily select some different numbers
> Pick any number, multiply the number by 3, add 6 to the product, divide the sum by 3, and subtract 2 from the quotient. See Example 5. (a) What is the relationship between the number you started with and the final number? (b) Arbitrarily select some diff
> In Exercises 37 and 38, estimate the maximum number of smaller figures (at left) that can be placed in the larger figure (at right) without the small figures overlapping.
> The chart on page 17 shows the calories burned per hour for an average person who weighs 150 lb. (a) Estimate the number of calories Phyllis, who weighs 150 lb, burns in a week if she lifts weight for 2 hours each week and jogs at 5 miles per hour for 4
> Land Ownership by the Federal Government The federal government owns a great deal of land in the United States. The graph below shows the percent of land owned by the federal government in the 12 states in which the federal government owns the greatest p
> A belief based on specific observations that has not been proven or disproven is called a conjecture or _________________.
