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physics
particle physics

Questions and Answers of Particle Physics

Show that it is possible to assign values of (B − L) (B is the baryon number and L is the lepton number) to the X and Y bosons in such a way that B − L is conserved for all the fundamental
Find two possible mechanisms for the decay p → π+ + ν̅e by suitably relabelling the lines in Figure 12.4(a) and (b). Check that the electric charge Q and the difference (B − L) are both
A high-energy beam of neutrons of intensity 106 /s traverses a target of 238U in the form of a thin foil whose density per unit area is 10−1 kg/m2. If the elastic and inelastic cross-sections are
For a free particle of momentum p = (px, py, pz), the Dirac equation has four independent solutions (1.12), where the independent spinors can be chosen to be of the formswhere ai, bi are finite
Generalise the discussion leading to the conservation of linear momentum (5.8) to the case of an N-particle system described by the wave function Ψ(r1, r2, r3, . . . , rN).
List the n = 3 states of positronium, together with their JPC values. What are their binding energies, neglecting fine structure?
Use lepton universality and lepton–quark symmetry to estimate the branching ratios for the decays b → c + e− + ν̅e (where the b and c quarks are bound in hadrons) and τ− → e− + ν̅e +
The \(x\) component of a car's velocity increases from 0 to \(+5.0 \mathrm{~m} / \mathrm{s}\) in \(1.0 \mathrm{~s}\), and then from \(+5.0 \mathrm{~m} / \mathrm{s}\) to \(+10 \mathrm{~m} /
Describe how to determine the \(x\) component of the position of an object at a specific instant, given(a) a graph of position \(x\) as a function of time \(t\) and(b) an equation for \(x(t)\).
In an \(x(t)\) curve, what is the significance of a steep slope as opposed to a gentle slope? What is the significance of a curve that slopes downward as you move from left to right along the time
What does it signify physically if the \(x\) component of an object's average velocity is negative over some time interval?
What is the relationship between the magnitude of a vector and the vector's \(x\) component?
What is the purpose of the unit vector \(\hat{\imath}\) ?
What is the mathematical meaning of the symbol \(\Delta\), the Greek capital letter delta?
Under what conditions is the \(x\) component of the displacement negative?
What is the shape of the \(x(t)\) curve for an object moving at constant velocity? What is the shape of the \(v_{x}(t)\) curve for this object?
Consider the point \(P\) located ahead of the wavefronts shown in Figure 34.3. Following the line of reasoning used in the preceding discussion, what can you say about the intensity (power/area, as
In discussing how a planar wave propagates, we could turn our earlier argument around and say that for each point \(\mathrm{Q}\) in Figure 34.2 there is a point \(\mathrm{S}\) somewhere on the
Does the spacing of the bright fringes in the twoslit arrangement in Figure 34.6 increase, decrease, or stay the same if we \((a)\) increase the spacing \(d\) of the slits, or \((b)\) increase the
Suppose there are three slits in a barrier on which light is incident normally, with each slit separated from its neighbor by a distance \(d\). Do the waves from all three slits cancel perfectly at
Why does the brightness of the fringes increase as the number of slits increases?
Suppose the light striking the reflective diffraction grating in Figure 34.13 is white light-that is, light consisting of all the colors of the rainbow. Red light has the longest wavelength of the
Diffraction gratings used in astronomical instruments must be able to separate wavelengths that are quite close together. (a) To increase the ability to do this, should the separation between slits
Considering only the top row of atoms in Figure 34.17, are there any other directions in which the \(x\) rays diffracted by the atoms interfere constructively? Figure 34.17 Diffraction of x rays by
Express the Bragg condition \(2 d \cos \theta=m \lambda\) in terms of the Bragg angle \(\alpha\) between the \(\mathrm{x}\) rays and the surface of the sample rather than the angle \(\theta\) between
While comparing the x-ray diffraction patterns from two crystals, you determine that crystal A produces a pattern with more widely spaced diffraction spots than crystal B. Which crystal has the
Spots in an electron diffraction pattern, such as that in Figure 34.23, move closer together as the speed of the electrons is increased. Does this mean the wavelength of the electrons increases or
How would the electron diffraction pattern in Figure 34.23 change if the electrons were traveling more slowly? Figure 34.23 Electron diffraction pattern for a diamond lattice. Notice the similarity
Compare the two-slit interference pattern obtained with electrons (Figure 34.25) with the two-slit interference pattern obtained with light (Figure 34.8). If light and electrons exhibit a similar
Figure 34.8 shows the interference pattern obtained by shining a strong laser beam on a pair of slits. If instead a very weak beam is shone on the same slits, so that the photons pass through the
How can the energy of the closed system made up of the two interfering waves remain constant (as the energy law states it must) if the maximum time-averaged intensity is four times the individual
As the above discussion indicates, the separation distance between the principal maxima for different wavelengths increases as the fringe order \(m\) increases. Can you obtain an arbitrarily great
When oil spreads on water, bands of different colors are visible. What causes the different colors?
Using Eq. 34.24, calculate the angle at which the first dark fringe occurs when(a) \(a(b) \(a \gg \lambda\). Interpret your results. sin 01 (first-order dark diffraction fringe). (34.24) a
Which of these three lenses offers (a) the highest resolution and(b) the lowest resolution: (i) \(f=10 \mathrm{~mm}, d=8 \mathrm{~mm}\); (ii) \(f=15 \mathrm{~mm}, d=10 \mathrm{~mm}\), (iii) \(f=20
(a) What does Figure \(34.48 b\) tell you about the relationship between the frequency of the incident light and the maximum kinetic energy of the ejected electrons? (b) What does the intercept of
A photon enters a piece of glass for which the index of refraction is about 1.5. What happens to the photon's (a) speed, (b) frequency, (c) wavelength, and (d) energy?
Coherent green light of wavelength \(540 \mathrm{~nm}\) passes through two narrow slits for which the center-to-center separation distance is \(150 \mu \mathrm{m}\). What is the difference in phase
A diffraction grating has adjacent slits separated by \(5.00 \mu \mathrm{m}\). When yellow light \((\lambda=570 \mathrm{~nm})\) is incident on the grating, what are the angular positions of the third
You shine a yellow laser beam on a diffraction grating and then shine a blue laser beam on the same grating. Is the spacing of the bright fringes for the yellow laser beam greater than, smaller than,
Light from a He-Cd laser \((\lambda=442 \mathrm{~nm})\) passing through a two-slit diffraction grating forms a pattern on a screen \(2.0 \mathrm{~m}\) away from the grating. If the first bright
A monochromatic \(x\)-ray beam that has a wavelength of \(0.5 \times 10^{-10} \mathrm{~m}\) strikes a sodium chloride crystal. The \(m=1\) Bragg angle is observed to be \(5.12^{\circ}\). What is (a)
In an x-ray diffraction experiment on a crystal that has a cubic lattice, the smallest Bragg angle at which you see a peak in the intensity of diffraction pattern is \(15.00^{\circ}\). If the
You are doing x-ray diffraction on a crystal that has a cubic structure, using \(0.1-\mathrm{nm} x\)-rays. If the two greatest Bragg angles at which you observe peaks in the intensity of the
How fast must a helium atom move in order to have a de Broglie wavelength of \(1.5 \times 10^{-10} \mathrm{~m}\) ?
What is the de Broglie wavelength of a \(0.43-\mathrm{kg}\) soccer ball moving at \(30 \mathrm{~m} / \mathrm{s}\) ?
An alpha particle, which consists of two neutrons and two protons, has a mass of \(6.645 \times 10^{-27} \mathrm{~kg}\). What is the de Broglie wavelength of an alpha particle that has been
You are using a \(2000 \mathrm{~V}\) potential difference to accelerate electrons toward a diffraction grating and produce a diffraction pattern. If you observe the first intensity peak at an angle
What is the smallest amount of (a) momentum and(b) energy that can be delivered using violet light for which \(\lambda=400 \mathrm{~nm}\) ?
At what rate do photons emitted by a laser \((\lambda=650 \mathrm{~nm})\) hit a wall \(3.00 \mathrm{~m}\) from the laser if the power rating is \(6.00 \mathrm{~mW}\) ? What assumption must you make
(a) What is the energy of a \(540-\mathrm{nm}\) photon emitted by a green laser source? (b) There are two green lasers that both emit \(540-\mathrm{nm}\) photons. Laser \(A\) has a power rating of
A red laser beam \((\lambda=647 \mathrm{~nm})\) is sent through a double slit to a screen that is \(15 \mathrm{~cm}\) wide and \(2.00 \mathrm{~m}\) away from the slits.(a) If the separation distance
Laser light passes through a double-slit barrier with slit separation \(d=0.120 \mathrm{~mm}\) onto a screen a distance \(L=6.00 \mathrm{~m}\) away. The distance between the central and first-order
Using a diffraction grating with 100 slits \(/ \mathrm{mm}\) to create a diffraction pattern on a screen \(2.50 \mathrm{~m}\) away from the grating, you see two neighboring bright fringes \(150
When a green laser light \((\lambda=550 \mathrm{~nm})\) shines on a fracture-line crack in a thin piece of metal, a diffraction pattern is observed on a screen located \(L=0.80 \mathrm{~m}\) from the
How wide does a single slit have to be so that \(684-\mathrm{nm}\) light passing through the slit has its first dark fringe \(20.0^{\circ}\) from the center of the interference pattern?
You send light through a slit that is \(150 \mu \mathrm{m}\) wide. What is the wavelength of the light that you must use so that the \(n=1\) fringes are \(1.8 \mathrm{~cm}\) apart on a screen \(2.0
Blue laser light \((\lambda=476.5 \mathrm{~nm})\) passes through a slit of width \(a=0.150 \mathrm{~mm}\). On a screen a distance \(L=2.500 \mathrm{~m}\) from the slit, what is the linear distance
Monochromatic \(647-\mathrm{nm}\) light is incident on a single slit. If the diffraction pattern is cast on a screen \(3.0 \mathrm{~m}\) from the slit, and the \(n=3\) dark fringe is \(2.5
What is the difference of the energies of a \(500-\mathrm{nm}\) photon and a \(600-\) nm photon?
What is the momentum of a photon that has energy of \(5.0 \times 10^{-15} \mathrm{~J}\) ?
When \(420-\mathrm{nm}\) light is incident on a sheet of metal, the electric potential needed to stop the electrons ejected from the metal surface is measured to be \(0.67 \mathrm{~V}\). What is the
You determine that the maximum wavelength of the light needed to eject electrons from the surface of a certain metal is \(683 \mathrm{~nm}\). What is the wavelength of the light if the potential
A double-slit barrier with slit separation distance \(d\) is a distance \(L\) from a screen, with \(L \gg d\). When green laser light \(\left(\lambda_{\mathrm{g}}=543 \mathrm{~nm}\right)\) passes
You cut a slit in a sheet of paper and use it to produce a diffraction pattern on a screen \(2 \mathrm{~m}\) away from the slit. If, using a laser of wavelength \(543.5 \mathrm{~nm}\), you measure a
When a laser beam of wavelength \(694 \mathrm{~nm}\) passes through a thin slit of width \(200 \mu \mathrm{m}\), what is the angular separation between the \(n=5\) dark fringe and the adjacent
Suppose a second bulb is added to the left of the one in Figure 33.1, as illustrated in Figure 33.3. What happens to(a) the brightness of the spot created on the screen by the first bulb and(b) the
Hold a piece of paper between your desk lamp (or any other source of light) and your desk or a wall. How does the sharpness of the edges of the shadow change as you move the paper closer to the bulb?
If the observer in Figure 33.8 moves to a different position, does the location of the image change? Figure 33.8 Diagrams showing the paths taken by light rays that are produced by a bulb and
In order for the person in Figure 33.14 to see a complete image of himself, does the mirror need to be as tall as he is? Figure 33.14 Paths taken by rays from more than one point on the object,
In vacuum, a particular light wave has a wavelength of \(400 \mathrm{~nm}\). It then travels into a piece of glass, where its speed decreases to two-thirds of its vacuum speed. What is the distance
Suppose the ray in Figure 33.16 travels in the opposite direction-that is, from the more dense medium to the less dense medium. If the angle of incidence is now \(\theta_{2}\), how does the angle of
When the ray reflected from the bottom surface in Figure 33.18 reemerges from the top surface, how does the angle it makes with the normal compare with \(\theta_{1}\) ? Figure 33.18 Olower
Because of dispersion, the critical angle for total internal reflection in a given medium varies with frequency. Is the critical angle for a violet ray greater or less than that for a red ray?
Sketch the wavefronts corresponding to all the rays in Figure 33.25a, both the parallel ones on the left and the refracted ones on the right. Figure 33.25 Converging lens with convex spherical
Do you need to draw all three principal rays to determine the location of an image?
As the object in Figure 33.31 is moved closer to the lens, does the size of the image increase, decrease, or stay the same? Figure 33.31 (a) When an object is located between the lens and the focus,
Is the image in Figure 33.33 real or virtual? Figure 33.33 Ray diagram for an object outside the focus of a diverging lens. For diverging lens, principal ray 3 points toward focus on other side of
(a) Draw the third principal ray in Figure 33.35. Is there any position for the object in Figure 33.35 for which (b) the image is larger than the object (c) the image is real? Figure 33.35 object
We found in Example 33.3 that a light ray is refracted twice when it passes completely through a slab of transparent material (see Figure 33.18). The result of these two refractions is that the
If the diverging lens in Figure 33.33 has a focal length of \(80 \mathrm{~mm}\) and the object is located \(100 \mathrm{~mm}\) from the lens, (a) what is the image distance and(b) how tall is the
A single-lens magnifying glass used to examine photographic slides produces eightfold angular magnification.(a) What is the lens strength in diopters? (b) What is the focal length of the lens?
(a) Consider replacing the objective lens in Fig. 33.48a with one that has a greater focal length, and moving the sample in order to keep it just outside the focal point of the lens. Does the image
A telescope with a magnification of \(22 \times\) has an eyepiece lens for which the focal length \(f_{2}\) is \(40.0 \mathrm{~mm}\). (a) What is the focal length \(f_{1}\) of the objective lens? (b)
An object is placed \(1.0 \mathrm{~m}\) in front of a diverging mirror for which the radius of curvature is \(1.0 \mathrm{~m}\).(a) Where is the image located relative to the mirror? Is the image
How should the lensmaker's formula be modified if a lens for which the index of refraction is \(n_{1}\) is submerged in a medium for which the index of refraction is \(n_{2}\) ?
Light is traveling at a speed of \(1.82 \times 10^{8} \mathrm{~m} / \mathrm{s}\) through a certain material. Determine what material it is likely traveling through.
What is the index of refraction of a material in which the speed of light is \(20 \%\) less than the speed of light in vacuum?
A red laser light has a wavelength of \(700 \mathrm{~nm}\) in air. What are the frequency and wavelength of this light in flint glass (index of refraction \(n=1.65\) )?
A light ray traveling through medium 1 with index of refraction \(n_{1}=1.70\) reaches the interface between medium 1 and medium 2 with index of refraction \(n_{2}=1.50\).(a) At what minimum angle
A light ray travels up from the bottom of a tank containing oil (index of refraction \(n=1.48\) ). If the oil surface is smooth, at what minimum angle from the normal to that surface would the light
You shine a laser pointer at an angle of \(30^{\circ}\) from the normal onto the surface of a thick block of glass for which the index of refraction is \(n=1.5\).(a) What is the angle of refraction
In vacuum, the wavelength of the red light in your laser pointer is \(680 \mathrm{~nm}\). Standing at the shore of a calm pond, you shine the laser beam onto the water surface at an angle of
Green laser light for which the wavelength in air is \(550 \mathrm{~nm}\) strikes a flint glass \(\left(n_{\text {glass }}=1.65\right)\) at an angle of \(50.0^{\circ}\) from the normal to the
A light ray travels through medium 1 , index of refraction \(n_{1}=1.5\), into medium 2, index of refraction \(n_{2}=2.4\) (Figure P33.55). At what angle with respect to the normal to the interface
A ray traveling through a large vat filled with medium 1 , index of refraction \(n_{1}=1.3\), is incident on a flat layer (thickness \(d=20 \mathrm{~mm}\) ) of medium 2, index of refraction
A child's toy sits on the bottom of a swimming pool in which the water \((n=1.33)\) depth is \(d=2.0 \mathrm{~m}\) (Figure P33.59). To a child standing at the pool edge and a distance \(h=3.6
What is the lens strength of a diverging lens that has a focal length of magnitude \(200 \mathrm{~mm}\) ?
What is the focal length of eyeglasses that have a lens strength of +2.5 diopters?
Using a converging lens that has focal length \(f=200 \mathrm{~mm}\), how far behind the lens do you expect to see a sharp image of an object located \(1.00 \mathrm{~m}\) in front of the lens?

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