An opaque screen contains a rectangular hole 0.199 mm (along the z-axis) by 0.100 mm (along the y-axis). It is illuminated by light at 543 nm from a heliumneon laser. A big positive lens with a...

Consider the Fraunhofer diffraction pattern of a rectangular aperture 0.200 mm (in the y-direction) by 0.100 mm (in the z-direction). It is formed in 543-nm light from a heliumneon laser, on a screen...

An angle has a value of 85. What is the angle in radians?

Figure P.10.28 is the irradiance distribution in the far field for a configuration of elongated rectangular apertures. Describe the arrangement of holes that would give rise to such a pattern and...

In Fig. P.10.29a and b are the electric field and irradiance distributions, respectively, in the far field for a configuration of elongated rectangular apertures. Describe the arrangement of holes...

The seesaw in Figure P8.28 is 4.5 m long. Its mass of 20 kg is uniformly distributed. The child on the left end has a mass of 14 kg and is a distance of 1.4 m from the pivot point while a second...

We wish to use the 15-cm-diameter objective from an amateur telescope to form an image on a CCD of a distant star. Assuming a mean wavelength of 540 nm and a focal length of +140 cm, determine the...

Consider the function and first check that the exponents are unitless. Then show that the Fourier transform of E(t) is You might want to use the integral identity ,-! E(t) = Ege-i@ote-7/27 E(@) =...

A telescope having an objective lens with a diameter of 10.0 cm will be used to view two equally bright small sources of 550-nm light. (a) Determine the angular separation of the sources if they are...

Sunlight impinges on a transmission grating that is formed with 5000 lines per centimeter. Does the third-order spectrum overlap the second-order spectrum? Take red to be 780 nm and violet to be 390...

A grating has a total width of 10.0 cm and contains 600 lines/mm. What is its resolving power in the second-order spectrum? At a mean wavelength of 540 nm, what wavelength difference can it resolve?

Collimated light from a krypton ion laser at 568.19 nm impinges normally on a circular aperture. When viewed axially from a distance of 1.00 m, the hole uncovers the first half-period Fresnel zone....

Imagine a point source S a perpendicular distance Ï 0 from a circular hole in an aperture screen Σ. The screen is a distance r 0 in front of an axial observation point-P. Show that...

Design a hydraulic lift that could be used to move a car. Assume the input piston the person would push on has an area of 0.10 m 2 . If you want a force of 300 N applied by the person to lift a car,...

Explain how Archimedess principle can be used to measure a persons percentage body fat. Fat has a different density than other body tissue.

Collimated red light (656.281 6 nm) from a hydrogen discharge lamp falls perpendicularly onto a transmission grating. The beam emerges forming a red line in the second-order spectrum at an angle of...

What will happen if water is poured on top of the mercury and ball bearing of Problem 78 such that the ball bearing is completely submerged in the water? Will the ball bearing (a) sink farther into...

Compute the Fourier transform of the triangular pulse shown in Fig. P.11.11. Make a sketch of your answer, labeling all the pertinent values on the curve. Fig. P.11.11 f(x) -L +L

Given that F{(x)} = F(), introduce a constant scaling factor 1/ and determine the Fourier transform of (x/). Show that the transform of (-x) is F(-).

What is the rotational kinetic energy of the Earth as it spins about its axis?

The rectangular function is often defined as where it is set equal to 1/2 at the discontinuities (Fig. P.11.14). Determine the Fourier transform of Notice that this is just a rectangular pulse, like...

The cat in Figure 9.21 undergoes free fall due to the force of gravity. Explain why we did not consider gravity when we discussed how the cat in Figure 9.21 managed to land on its feet. Figure 9.21...

When a spinning figure skater pulls her arms close to her body (Fig. 9.11), she spins faster. If she then pushes her arms away from her body, her angular velocity decreases. Her rotational kinetic...

The displacement of a harmonic oscillator is given by y = 7.1 sin(48t), where the units of y are meters and t is measured in seconds. Give three values of t at which the oscillator has (a) Its...

A simple pendulum has a period of 2.5 s on the Earth. An astronaut then takes it to the surface of the Moon. What period does the astronaut measure there?

The cone of a loudspeaker oscillates with an amplitude of 2.0 mm. If the frequency is 2.5 kHz, what are the maximum velocity and the maximum acceleration of the cone? Assume the speaker cone moves as...

Under normal atmospheric conditions, the surface of the Earth is negatively charged. What is the direction of the electric field near the Earths surface?

Four point particles are located at the corners of a square (Fig. P17.15). The two particles on the left each carry a charge +Q. If the electric field at the center of the square is directed to the...

Two particles of charge Q and 5Q are located as shown in Figure P17.16. When a third charge is placed at the origin, it is found that the force on it is zero. Find a. Figure P17.16 ? y - L -L x. 5Q

An electron and a proton are a distance r = 7.5 10 -9 m apart. How much energy is required to increase their separation by a factor of two?

If the length of a wire is increased by a factor of 4, by what factor does the resistance change?

There is a potential difference of V 20 V across a resistor with R = 50. What is the current through the resistor?

If a current of 0.10 A flows through a resistor and the potential drop across the resistor is 1.5 V, what is the resistance?

Consider the configuration of resistors shown in Figure P19.108. Each connection can have a resistor that is disconnected or whose value is 5.0 or 10.0. To determine the value of each resistor or...

An electron is moving in the xy plane with its velocity along the -y direction. If the magnetic force on the electron is in the +z direction when B(vector) direction. If the magnetic force on the...

Faraday and many other scientists expected that there should be a certain symmetry between electric and magnetic phenomena. Is there a magnetic analog of electric charge? That is, is there such a...

In an electric circuit containing inductors, the largest induced voltage usually occurs just after a switch is opened or closed. Explain why.

An inductor has the form of a coil with 2000 turns and a diameter of 1.5 mm. The inductor is placed in a magnetic field perpendicular to the plane of the coil and increasing at a rate of 0.35 T/s....

Some resistors are made from a coil of wire. What is the best way to model the circuit behavior of such a resistor? Choose one answer and explain. (a) As an ideal resistor in series with an ideal...

Find the RL time constant for decay of the current in the circuit in Figure 21.25B. Express your answer in terms of the values of the resistances R 1 and R 2 , and the inductance L. R2 R1

Figure P23.2 shows the directions of the electric and magnetic fi elds associated with several different electromagnetic waves. What are the directions of propagation of these waves? Case 1 Case 2...

The human nose is very sensitive to certain molecules. For example, it can sense the presence of the chemical CH 3 SH (methyl mercaptan) at levels as small as 2 parts per billion. Another especially...

Bug breath. Insects do not have lungs or a blood circulatory system. Instead, a system of openings in the exoskeleton (spiracles) lead to branching tubes of decreasing diameter called trachea, the...

Consider the common expressions (a) Theres no such thing as a free lunch and (b) You cant even break even. Which of the laws of thermodynamics might these expressions refer to? Explain.

Describe a simple U-tube manometer.

Describe a differential U-tube manometer.

Describe a well-type manometer.

Describe an inclined well-type manometer.

Three surfaces of an instrument package are cooled by soldering half-sections of copper tubing to it as shown in Fig. 9.31. Compute the Reynolds number for each section if ethylene glycol at 77?F...

A hydraulic oil is flowing in a drawn steel hydraulic tube with an OD of 50 mm and a wall thickness of 1.5 mm. A pressure drop of 68 kPa is observed between two points in the tube 30 m apart. The oil...

Find the flow rate of water at 60?F in each pipe of Fig. 12.12. 0.3 ft/s 50 ft 50 ft 1.2 ft/s 30 ft 30 ft 50 ft 50 ft All pipes 25-in Schedule 40 0.3 ft/s 0.6 ft/s

A 2-kg brick has the dimensions 7.5 cm 15 cm 30 cm. The pressure the brick exerts on the ground when standing on its smallest face is a. 0.0178 Pa b. 0.0225 Pa c. 178 Pa d. 225 Pa

Which of the following isomeric carbocations is the most stable? CH,+ CH3 () (b) -CH3 CH3 () (d)

Write all sensible products of the reaction of each of the alcohols in Problem 31 with concentrated aqueous HBr. In Problem 31 OH () CH-CH-CH,O (b) CH;CHCH3 (c) CH;CH,CH,CH,OH OH (d) (CH),C, ()...

Give detailed mechanisms and final products for the reaction of 3-methyl-2-pentanol with each of the reagents that follow. (a) NaH (b) Concentrated HBr (c) PBr 3 (d) SOCl 2 (e) Concentrated H 2 SO 4...

What are the most likely product(s) of each of the following reactions? CH3 CH3 Conc. HI CH,CH,OH, H,SO, () HO (b) CH;CCH,OH CH3 CH,OH CH3 I Conc. H.SO, 180 () (d) CH, CH, H3

Suggest the best syntheses for each of the following ethers. Use alcohols or haloalkanes or both as your starting materials. () (b) () (d) () (f)

Propose syntheses of the following molecules, choosing reasonable starting materials on the basis of the principles of synthetic strategy introduced in preceding chapters, particularly in Section...

Give efficient syntheses of each of the following compounds, beginning with the indicated starting material. (a) trans-1-Bromo-2-methylcyclopentane, from cis-2-methylcyclopentanol (b) (c)...

Without consulting the Reaction Road Map on pp. 556 557, suggest a reagent to convert a general alkene, into each of the following types of compounds. H C=C

Give the expected product of reaction of 2-methyl-1-pentene with each of the following reagents. (a) H 2 , PtO 2 , CH 3 CH 2 OH (b) D 2 , Pd C, CH 3 CH 2 OH (c) BH 3 , THF then NaOH + H 2 O 2 (d)...

Compare the C2 C3 bonds in propane, propene, and propyne. Should they be any different with respect to either bond length or bond strength? If so, how should they vary?

What are the products of reaction of (E)-3-methyl-3-hexene with each of the reagents in Problem 46? (a) H 2 , PtO 2 , CH 3 CH 2 OH (b) D 2 , Pd C, CH 3 CH 2 OH (c) BH 3 , THF then NaOH + H 2 O 2 (d)...

Write the mechanism and final product for the reaction of 1-propynyllithium with trans-2,3- dimethyloxacyclopropane.

Show how the Heck reaction might be employed to synthesize each of the following molecules. doCH, () COCH3 (b)

The compound whose structure is H C C(CH 2 ) 3 Cl is best named (IUPAC) (a) 4-chloro-1-pentyne; (b) 5-chloropent-1-yne; (c) 4-pentyne-1-chloroyne; (d) 1-chloropent-4-yne.

A nucleophile made by deprotonation of propyne is (a) :CH,CH;; (b) :HC=CH;; (c) :C=CH; (d) :C=CCH; (e) :HC=CHCH3.

Compare the allylic bromination reactions of 1,3-pentadiene and 1,4-pentadiene. Which should be faster? Which is more energetically favorable? How do the product mixtures compare? NBS, ROOR, CCI...

The ratio of 1,2- to 1,4-addition of Br 2 to 1,3-butadiene is temperature dependent. Identify the kinetic and thermodynamic products, and explain your choices.

Reaction review. Without consulting the Reaction Road Map on p. 721, suggest a reagent to convert benzene into each of the following compounds. C(CH3)3 NO2 CH3 CH,CH; SO,H Br (e) (f) (h)

The rate of nitration of (chloromethyl)benzene, shown below is 0.71 relative to the rate of nitration of benzene (=1). The (chloromethyl)nitrobenzene product mixture that results contains 32% ortho,...

Specify whether you expect the benzene rings in the following compounds to be activated or deactivated. NO2 OH (a) (b) 'NO2 CH3 COOH NH2 SO-H HO C(CH3)3 (d) (e) (f) 'NO2 H3

Rank the compounds in each of the following groups in order of decreasing reactivity toward electrophilic aromatic substitution. Explain your answers. CH3 () (b) H; H3

Write the structure(s) of the major product(s) that you expect from each of the following electrophilic aromatic substitutions. (a) Nitration of methylbenzene (toluene); (b) sulfonation of...

Draw appropriate resonance forms to explain the activating ortho, para-directing character of the phenyl substituent in biphenyl Biphenyl

(a) When a mixture containing one mole each of the three dimethylbenzenes (o-, m-, and p-xylene) is treated with one mole of chlorine in the presence of a Lewis acid catalyst, one of the three...

Describe the experimental conditions that would be best suited for the efficient synthesis of each of the following compounds from the corresponding nonhalogenated ketone. (a) (b) (c) Br O CH;CHCCH3

Formulate a mechanism for the acid-catalyzed hydrolysis of the pyrrolidine enamine of cyclohexanone (shown in the margin). + H,O H+ 'N' H

When 2-methylcyclopentanone is treated with the bulky base triphenylmethyllithium under the two sets of conditions shown, the two possible enolates are generated in differing ratios. Why is this so?...

Name or draw the structure of each of the following compounds. (a) (b) (c) (d) (e) (f) (e) (Z )-2-Acetyl-2-butenal (f) trans-3-Chlorocyclobutanecarbaldehyde (CH3),CHCCH(CH;)2

For each of the following molecules, propose two methods of synthesis from the different precursor molecules indicated. (a) CH 3 CH=CHCH 2 CH(CH 3 ) 2 from (1) an aldehyde and (2) a different...

When 1,4- and 1,5-dicarboxylic acids, such as butanedioic (succinic) acid (Section 19-8), are treated with SOCl2 or PBr3 in attempted preparations of the diacyl halides, the corresponding cyclic...

Reaction review II. Without consulting the Reaction Road Map on p. 915, suggest reagents to convert hexanoic acid into each of the following compounds: (a) 1-hexanol; (b) hexanoic anhydride; (c)...

Give the product(s) of reaction of hexanal with each of the following reagents. (a) HOCH 2 CH 2 OH, H + (b) LiAlH 4 , then H + , H 2 O (c) NH 2 OH, H + (d) NH 2 NH 2 , KOH, heat (e) (CH 3 ) 2 CHCH 2...

(a) Write a mechanism for the esterification of propanoic acid with 18 O-labeled ethanol. Show clearly the fate of the 18 O label. (b) Acid-catalyzed hydrolysis of an unlabeled ester with 18...

Interpret the labeled peaks in the mass spectrum of 2-methylhexanoic acid (MS-H). 74 100 MS CH;CH,CH,CH,CHCOOH 50 CH3 87 45 130 20 40 60 80 100 120 140 160 mlz MS-H Relative abundance

Propose a short synthesis of 2-butynoic acid, CH3CqCCO2H, starting from propyne.

What is the IUPAC name of the compound shown? (a) (E )-3-Methyl-2-hexenoic acid (b) (Z )-3-Methyl-2-hexenoic acid (c) (E )-3-Methyl-3-hexenoic acid (d) (Z )-3-Methyl-3-hexenoic acid H;C CO.H C=C...

Give the product of reaction of cyclopentanecarboxylic acid with each of the reagents in Problem 40. Data From problem 40 (a) SOCl2 (b) PBr3 (c) CH3CH2COBr 1 pyridine (d) (CH3)2CHOH 1 HCl (e) (f)...

When methyl ketones are treated with a halogen in the presence of base, the three hydrogen atoms on the methyl carbon are replaced to give a CX 3 -substituted ketone. This product is not stable under...

Show how the Hell-Volhard-Zelinsky reaction might be used in the synthesis of each of the following compounds, beginning in each case with a simple monocarboxylic acid. Write detailed mechanisms for...

The Hell-Volhard-Zelinsky reaction produces only bromocarboxylic acids. However, modifi ed procedures have been developed to convert acyl chlorides into a-chloro- and a-bromoacyl chlorides by...

Illustrate by means of appropriate structures (including all relevant resonance forms) the initial species formed by (a) breaking the weakest C H bond in 1-butene; (b) treating 4-methylcyclohexene...

Rank primary, secondary, tertiary, and allylic radicals in order of decreasing stability. Do the same for the corresponding carbocations. Do the results indicate something about the relative ability...

Formulate a mechanism for the formation of acetamide, from methyl acetate and ammonia. CH;CNH2

Show how you might synthesize chlorpheniramine, a powerful antihistamine used in several decongestants, from each of carboxylic acids A and B. Use a different carboxylic amide in each synthesis. N-...

Give the structure of the product of the fi rst of the following reactions, and then propose a scheme that will ultimately convert it into the methyl-substituted ketone at the end of the scheme. This...

Give structures that correspond to each of the following names. (a) N,N-Dimethyl-3-cyclohexenamine; (b) N-ethyl-2-phenylethylamine; (c) 2-aminoethanol; (d) m-chloroaniline.

Give the structures of all possible nitrogen-containing organic products that might be expected to form on reaction of chloroethane with ammonia.

Suggest the best syntheses that you can for the following amines, beginning each with any organic compounds that do not contain nitrogen. (a) Butanamine; (b) N-methylbutanamine; (c)...