The product of any two counting numbers is divisible by 2.
> 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?
> 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?
> 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.
> 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 _________________.
> In Exercises 35 and 36, draw the next diagram in the pattern (or sequence).
> Gaining Weight The graph below shows that as a society we tend to get heavier as we grow older. Also, with age, the amount of muscle tends to drop, and fat accounts for a greater percentage of weight. (a) Estimate the average percent of body fat for a wo
> Broadway Tickets The graph below shows the average ticket price for a show on Broadway for each season from 2009 through 2014. (a) Assuming this trend continues, use the graph to predict the average ticket price for a show on Broadway for the 2015 seaso
> An Aging Population The bar graph below shows population figures for 1900 and 2000 and estimated population figures for 2050. (a) Estimate the number of people 65 and older in 1900. (b) Estimate the number of people 65 and older in 2050. (c) Estimate the
> Video Games the graph below shows the amount of money spent in the United States on video games played on mobile devices in 2013 and the projected amount for the years 2014–2018. (a) Assuming this trend continues, use the graph to predi
> Exercising The circle graph below shows the biggest obstacles to sticking to an exercise program, as reported by 2987 employees at the CDA Corporation. (a) Estimate the number of adults surveyed who don’t have the energy to exercise. (b
> Triangles in a Triangle Four rows of a triangular figure are shown. (a) If you added six additional rows to the bottom of this triangle, using the same pattern displayed, how many triangles would appear in the 10th row? b) If the triangles in all 10 row
> Coffee Consumption The circle graph below shows the number of cups of coffee consumed per week by people in the United States. Assume 700 people were surveyed. (a) Estimate the number of people surveyed who consume 5–7 cups of coffee pe
> Quilt Design the pattern shown is taken from a quilt design known as a triple Irish chain. complete the color pattern by indicating the color assigned to each square.
> The Olympic Peninsula Following is a map of the Olympic Peninsula in the state of Washington. Using the scale on the map, estimate the distance of the route shown in red, starting at Forks and ending at Sequim, passing through Port Angeles.
> 26.9 + 67.3 + 219 + 143.3
> A Triangular Pattern The ancient Greeks labeled certain numbers as triangular numbers. The numbers 1, 3, 6, 10, 15, 21, and so on are triangular numbers. (a) Can you determine the next two triangular numbers? (b) Describe a procedure to determine the nex
> The Pacific Coast Highway Below is a map of California’s scenic Pacific Coast Highway. Using the scale on the map, estimate the distance between Carmel- by-the-Sea and Hearst Castle.
> A Square Pattern The ancient Greeks labeled certain numbers as square numbers. The numbers 1, 4, 9, 16, 25, and so on are square numbers. (a) Determine the next three square numbers. (b) Describe a procedure to determine the next five square numbers with
> The Cost of a Vacation The Kleins are planning a vacation in the Great Smoky Mountains National Park. Their round-trip airfare from Houston, Texas, to Knoxville, Tennessee, totals $973. Car rental is $61 per day and lodging is a total of $97 per day, and
> (a) Select a variety of one- and two-digit numbers between 1 and 99 and multiply each by 9. Record your results. (b) Find the sum of the digits in each of your products in part (a). If the sum is not a one-digit number, find the sum of the digits of t
> Currency Estimate the difference in the value of 50 U.S. dollars and 100 Mexican pesos. Assume that one Mexican peso is about 0.068 U.S. dollar.
> Find the letter that is the 118th entry in the following sequence. Explain how you determined your answer. Y, R, R, Y, R, R, Y, R, R, Y, R, R, Y, R, R, ….
> Estimating Time Donna is a long-distance runner, whose average time per mile in marathons is 9 minutes, 55 seconds. Estimate the time it will take her to complete a 26-mile, 385-yard (or ≈ 26.2-mile) marathon
> Use inductive reasoning to predict the next three numbers in the pattern (or sequence).
> Picking Strawberries Chuck hires 11 people to pick strawberries from his field. He agrees to pay them $1.50 for each quart they pick. Estimate the total amount of money he will have to pay if each person picks 8 quarts.
> A specific case that satisfies the conditions of a conjecture but shows the conjecture is false is called a _____________.
> Use inductive reasoning to predict the next three numbers in the pattern (or sequence). 1, 1, 2, 3, 5, 8, 13, 21, …..
> Estimating Weights In a tug of war, the weight of the members of the two three-person teams is given below. Estimate the difference in the weights of the teams.
> Use inductive reasoning to predict the next three numbers in the pattern (or sequence). 0, 1, 3, 6, 10, 15, …..
> Monthly Expenses Li’s total monthly expenses consist of room and board: $595; car payment: $289; gas: $120; insurance: $110; and miscellaneous expenses: $230. Estimate Li’s total monthly expenses.
> Use inductive reasoning to predict the next three numbers in the pattern (or sequence). 1, 4, 9, 16, 25, …..
> The number of months needed to save $400 if you save $23 each month
> Use inductive reasoning to predict the next three numbers in the pattern (or sequence). 5, −25, 125, −625, ….
> A 15% tip on a meal that costs $26.32
> Use inductive reasoning to predict the next three numbers in the pattern (or sequence).
> The weight of one pork chop in a package of six pork chops if the weight of the package is 3.25 lb
> The symbol ≈ means is approximately ________________ to.
> Use inductive reasoning to predict the next three numbers in the pattern (or sequence). 7, 5, 3, 1, …
> The total weight of three people on an elevator if their weights are 95 lb, 127 lb, and 210 lb
> Use inductive reasoning to predict the next three numbers in the pattern (or sequence). 5, −5, 5, −5, …..
> The cost of 5 items purchased at a hardware store if the items cost $1.29, $6.86, $12.43, $25.62, and $8.99
> Use inductive reasoning to predict the next three numbers in the pattern (or sequence). 4, 7, 10, 13, …
> The cost of 5 items at a grocery store if the items cost $7.99, $4.23, $16.82, $3.51, and $20.12
