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physics
modern physics

Questions and Answers of Modern Physics

Explain the following observations, in words, concerning the NOE in a two-spin system. (a) In a transient NOE experiment, and in the initial rate, the NOE enhancement depends only on the
For the molecule shown opposite, a transient NOE experiment (recorded in the initial rate limit) in which HB was inverted gave equal NOE enhancements (in the initial rate limit) on HA and HC. If HA
For a two-spin system, and in the initial rate, show that in the NOESY experiment, changing the phase of the first pulse from x to -x, changes the sign of the diagonal and cross peaks, but leaves the
In the case of relaxation caused by random fields, calculate the value of B2loc needed to give a proton T1 of 1 s at a Larmor frequency of 500 MHz and for a correlation time of 10 ps. Comment on your
In a spin echo experiment designed to measure the value of RXY, the following peak heights S(Ï„) were measured as a function of the spin echo delay Ï„. Use a graphical method to
Show that, for a fixed frequency to ω, the maximum in the reduced spectral density function j(ω) occurs at Jc = \1/ω. What is the significance of this result?
For a sample consisting of isolated spins, explain in words why it is necessary for the rate constant for the relaxation-induced transitions from the α state to the β state to be less than the rate
In an inversion-recovery experiment the following peak heights S(Ï„) (arbitrary units) were measured as a function of the delay Ï„:Use a graphical method to analyse these data and
In an experiment to estimate T1 using the inversion-recovery sequence, three peaks in the spectrum were observed to go through a null at 0.5, 0.6 and 0.8 s, respectively. Explain how an estimate for
An alternative to the inversion-recovery method for estimating Rz is the saturation-recovery experiment. This starts with the spin being irradiated for a long time so that it becomes saturated, i.e.
Using the approach of section 9.6.2 on page 269, write down expressions for dni/dt for each of the four levels in terms of the populations and the transition rate constants, W.
In this exercise we will use the expressions given in section 9.6.3 on page 271 and in section 9.8.5 on page 296 to calculate the relaxation rate constants which arise from the dipolar relaxation of
The typical separation of a directly bonded l3C-1H pair is 1.1 A. Assuming a correlation time of 20 ps (i.e. the fast motion limit), calculate values for the rate constants Rz(1), Rz(2) σ12, Rxy(1)-
Draw sketches, roughly to scale, of the multiplets represented by the following operators:and assuming that the couplings constants are: (a) J12 = 2Hz, J23 = 6 Hz; and (b) J12 = 6 Hz, J23 - 6 Hz.
In the ZCOSY experiment, work out the contribution which the operator product 1+ 2β3α, present during t1, makes to the 1-2 cross peak. Compare your answer with that in the previous question.
The pulse sequence for a constant time version of double-quantum filtered COSY is shown below.Show that, for a two-spin system and starting from z, the double quantum present between the final two
Starting from 1z, determine the form of a constant time COSY spectrum for a three-spin system. Comment on the choice of the fixed time T for such a spin system.
Consider the three-spin system opposite which consists of a proton I coupled to a 13C, S1, with coupling constant j1S1; S1 is further coupled to a second l3C, S2, with coupling constant JS1,S2- Note
Using the same approach as in Fig. 10.30 on page 361, verify that the following transfers take place:Work out which two line-selective 180° pulses you could need to cause transfer from: (a) 1-3
Verify that the operators given at the start of section 10.9.4 on page 364 are indeed those present at the end of t1. By combining the trigonometric functions in the usual way, also verify that Eq.
Using the same approach as in section 10.9.4 on page 364, determine the form of the two-dimensional multiplets arising from the combinations S3 and S4, and hence verify that by further combining
Can you think of any disadvantages of the TROSY HSQC sequence, when applied to l5N-1H correlation?
Starting with the operator hy, work out the result of evolution of the 1-2, 1-3 and 2-3 couplings for a time t. Comment on the operators you obtain and the trigonometric factors associated with
Starting with the operator 223z, draw up a tree diagram to show the evolution under first the 2-3 coupling, and then the 1-2 coupling. You do not need to work out all the sines and cosines to draw
In a COSY of a three-spin system, the diagonal peak of spin one is represented by term |1] on page 326. From this term, work out the detailed form of the diagonal-peak multiplet, using the same
Identify all four anti-phase square arrays in each of the multiplets shown in Fig. 10.8 on page 329. Sketch the form of the 1-2 cross peak for the following combinations of couplings: (a) J12 = 8 Hz,
Assuming that spin three is a heteronucleus, sketch the form of the reduced 1-2 cross-peak multiplets which would be expected for the cross peaks shown in Fig. 10.8 on page 329. Identify the two
Explain why, whereas it is not usually possible to measure a value for the active coupling constant responsible for a cross peak, it is sometimes possible to measure values of the passive coupling
In a three-spin system, give an interpretation of each of the following products of polarization operators. State, with reasons, which of the products are observable.Give the time evolution of the
In a small flip angle COSY experiment, work out the contribution which the operator product 1+ 2β3α, present during t1, makes to the 1-2 cross peak. You should follow the same approach as used
Using the same approach as was used to derive Eq. 11.3 on page 383, show that a z-rotation through an angle É¸ of the operator i- generates a phase factor of exp(+i
Consider the pathway shown below for a heteronuclear experiment.Write down the spatially dependent phase which accrues during the two gradient pulses, and hence determine the ratio (G1T1)/(G2T2)
Draw up coherence transfer pathways for the following experiments, and explain how gradients could be used to select the specified pathways. In some cases you may need to modify the pulse sequences,
Draw up coherence transfer pathways for the following experiments: (a) triple-quantum filtered COSY (which is identical to DQF COSY, except that p = ±3 between the last two pulses); (b) zero-quantum
Confirm that each of the combinations of A and B given in the table on p. 393 does indeed give rise to a spectrum with the same lineshape. Draw up a diagram, similar to that of Fig. 11.6 on page 394,
In section 11.5.1 on page 396 it was shown that a pathway with Δp = -3 could be selected with the following four-step cycle. pulse phase: [0°, 90°, 180°, 270°] rx phase: [0°, 270°, 180°,
In section 11.5.2 on page 399 it was shown how the independent completion of two four-step cycles, the first selecting Δp = +1 and the second selecting Δp = -2, generates a 16-step cycle. Draw up a
Consider a phase cycle in which the pulse phase goes through the three steps [0°, 120°, 240° ]. Devise a set of accompanying receiver phase shifts (which will not be multiples of 90°) which will
Shown below are the pulse sequence and coherence transfer pathway for triple-quantum filtered COSY.Grouping the first two pulses together, devise a six-step phase cycle which will select the required
For the NOESY experiment, group the first two pulses together and devise a four-step phase cycle which selects the pathway shown in Fig. 11.15 on page 407. Add axial peak suppression to your cycle
Consider the pathway shown below.Write down the spatially dependent phase which accrues during the two gradient pulses, and hence determine the ratio (G2T2)/(G1T1) which will refocus the
For each of the following molecules determine which groups of protons or l9F nuclei (if any) are chemically or magnetically equiv¬alent, giving your reasons. Hence describe each spin system using
For the ABX spectrum shown in Fig. 12.27 the frequencies of the lines, relative to some arbitrary origin, are given in the following table.(a) From the AB part, pick out the lines which correspond to
Consider a spin system consisting of a l3C, spin X, and two protons, A and B. The carbon has a one-bond coupling of 150 Hz to proton A, and a long-range coupling of 15 Hz to proton B. Protons A and B
This question is concerned with an l2S spin system.(b) By first applying the identity cos2 (A) = ½ j[l + cos(2A)], and then the identity cos (A)cos(B) = 1/2 [cos (A + B) + cos (A - B)], show
Using the same approach as in the previous exercise, predict the form of the multiplets arising from the terms x, 21Zx, 41z2zx and 81z2z3zx m an I3S spin system; compare your results with Fig. 12.6
(a) Compute the evolution of the operator y under the influence of the I-S couplings in (i) an IS, (ii) an I2S and (iii) an I3S spin system. (b) Compute the evolution of the operator 81z2z3zy
On page 457 it was shown that for a spin echo applied to an I3S spin system the amount of the singly anti-phase terms goes as cos2 (2πJ τ) sin (2πJ τ). Maximizing this function is equivalent to
In an APT experiment the delay τ has to be set to a compromise value based on the average value of a one-bond C-H coupling. Suppose that we take this value to be 130 Hz, what will be the value for
Predict the form of the cross-peak multiplet that would be seen in a COSY spectrum of an I2S and of an I$S spin system, assuming that the I and S spins are affected by both 90° pulses. [The
In an AB spectrum the two weaker lines are found to have frequen¬cies of 40.8 Hz and 9.18 Hz, and the two stronger lines are found to have frequencies of 31.1 Hz and 18.7 Hz, measured relative to
(a) Using EXCEL (or some other suitable program) set up aspreadsheet which computes the line frequencies and inten¬sities of both the AB and X parts of an ABX system for an arbitrary set of
You have been offered a superconducting magnet which claims to have a homogeneity of '1 part in 108'. Your intention is to use it to record 31P spectra at Larmor frequency of 180 MHz, and you know
A careful pulse calibration experiment has determined that the 180° pulse length is 24.8 pis. How much attenuation, in dB, would have to be introduced into the transmitter in order to give an RF
A spectrometer is equipped with a transmitter capable of generat¬ing a maximum of 100 W of RF power at the frequency of l3C. Using this transmitter at full power, the 90° pulse width is found to be
Explain what is meant by 'a two-bit ADC and draw a diagram to illustrate the outcome of such a ADC being used to digitize a sine wave. Why is it generally desirable to use an ADC with the largest
A spectrometer operates at 800 MHz for proton, and it is desired to record a spectrum covering a shift range of 15 ppm. Assuming that the receiver reference frequency is placed in the middle of this
1. Which of the following is the frequency of the musical note C5? a) 376 g b) 483 m/s c) 523 Hz d) 26.5 J 2. If A and B are vectors and B = -A, which of the following is true? a) The magnitude of B
What angle does A = (Ax, Ay) = (30.0 m,-50.0 m) make with the positive x-axis? What angle does it make with the negative y-axis?
Sketch the vectors with the components A = (Ax,Ay) = (-30.0 m, -50.0 m) and B = (Bx,By) = (30.0 m, 50.0 m), and find the magnitudes of these vectors.
What angle does B = (Bx, By) = (30.0 m, 50.0 m) make with the positive x-axis? What angle does it make with the positive y-axis?
Find the magnitude and direction of each of the following vectors, which are given in terms of their x- and y-components: A = (23.0, 59.0), and B = (90.0, -150.0).
Find the magnitude and direction of-A + B, where A = (23.0, 59.0), B = (90.0,-150.0).
Find the magnitude and direction of -5A + B, where A = (23.0, 59.0), B = (90.0,-150.0).
Find the magnitude and direction of -7B + 3A, where A = (23.0, 59.0), B = (90.0,-150.0).
Which of the six cases shown in the figure has the largest absolute value of the scalar product of the vectors A and B?
Which of the six cases shown in the figure has the smallest absolute value of the scalar product of the vectors A and B?
Which of the six cases shown in the figure has the largest absolute value of the vector product of the vectors A and B?
Which of the six cases shown in the figure has the smallest absolute value ot the vector product of the vectors A and B?
Rank order the six cases shown in the figure from the smallest absolute value to the largest absolute value of the scalar product of the vectors A and B.
Rank order the six cases shown in the figure from the smallest absolute value to the largest absolute value of the vector product of the vectors A and B.
Toward the end of their lives many stars become much bigger. Assume that they remain spherical In shape and that their masses do not change in this process. If the radius of a star increases by a
Toward the end of their lives many stars become much bigger. Assume that they remain spherical in shape and that their masses do not change in this process. If the circumference of a star increases
Toward the end of their lives many stars become much bigger. Assume that they remain spherical in shape and that their masses do not change in this process. If the volume of a star increases by a
Toward the end of their lives many stars become much bigger. Assume that they remain spherical in shape and that their masses do not change in this process. If the surface area of a star increases by
1. How many watts are in 1 gigawatt (GW)?a) b) 106c) 109d) 1012e) 10152. What is the limit of γ = 1/√1 - (v/c)2, where c is a constant and v → 0?a) γ = 1b) γ = 0c) γ = 2d) γ = ve) γ = v/23.
In Europe, cars' gas consumption is measured in liters per 100 kilometers. In the United States, the unit used is miles per gallon.a) How are these units related?b) How many miles per gallon does
If you draw a vector on a sheet of paper, how many components are required to describe it? How many components does a vector in real space have? How many components would a vector have in a
Since vectors in general have more than one component and thus more than one number is used to describe them, they are obviously more difficult to add and subtract than single numbers. Why then work
If A and B are vectors specified in magnitude-direction form, and C = A + B is to be found and to be expressed in magnitude-direction form, how is this done? That is, what is the procedure for adding
Suppose you solve a problem and your calculator's display reads 0.0000000036. Why not just write this down? Is there any advantage to using the scientific notation?
Since the British system of units is more familiar to most people in the United States, why is the international (SI) system of units used for scientific work in the United Slates'
Is it possible to add three equal-length vectors and obtain a vector sum of zero? If so, sketch the arrangement of the three vectors. If not, explain why not.
Two flies sit exactly opposite each other on the surface of a spherical balloon. It the balloon's volume doubles, by what factor does the distance between the flies change?
What is the ratio of the volume of a cube of side r to that of a sphere of radius r? Does your answer depend on the particular value of r?
Consider a sphere of radius r. What is the length of a side of a cube that has the same surface area as the sphere?
The mass of the Sun is 2 ∙ 1030 kg, and the Sun contains more than 99% of all the mass in the Solar System. Astronomers estimate there are approximately 100 billion stars in the Milky Way and
A futile task is proverbially said to be "like trying to empty the ocean with a teaspoon." Just how futile is such a task? Estimate the number of teaspoonfuls of water in the riarth's oceans.
The world's population passed 6.5 billion in 2006. Estimate the amount of land area required if each person were to stand in such a way as to be unable to touch another person. Compare this area to
Advances in the field of nanotechnology have made it possible to construct chains of single metal atoms linked one to the next. Physicists are particularly interested in the ability of such chains to
One of the standard cliches in physics courses is to talk about approximating a cow as a sphere. How large a sphere makes the best approximation to an average dairy cow? That is, estimate the radius
Estimate the mass of your head. Assume that its density is that of water, 1000 kg/m3.
Estimate the number of hairs on your head.
How many significant figures are in each of the following numbers? a) 4.01 b) 4.010 c) 4 d) 2.00001 e) 0.00001 f) 2.1 - 1.10042 g) 7.01 ∙ 3.1415
Two different forces, acting on the same object, are measured. One force is 2.0031 N and the other force, in the same direction, is 3.12 N. These are the only forces acting on the object. Find the
Given the equation w = xyz, and x = 1.1 - 103, y = 2.48 - 10-2, and z = 6.000, what is w, in scientific notation and with the correct number of significant figures?
How many inches are in 30.7484 miles?
The masses of four sugar cubes are measured to be 25.3 g, 24.7 g, 26.0 g, and 25.8 g. Express the answers to the following questions in scientific notation, with standard SI units and an appropriate
What is the surface area of a right cylinder of height 20.5 cm and radius 11.9 cm?
You stop on your brand-new digital bathroom scale, and it reads 125.4 pounds. What is your mass in kilograms?

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