代做Physics 2: Physical Science & Technology (PHYC10004) Week 10代写留学生Matlab语言

日期：2025-11-15 12:19

Physics 2: Physical Science & Technology (PHYC10004)

Week 10

Discussion Questions

1

If an electron and proton have the same kinetic energy, which then has the greater de Broglie wavelength?

2

Can a photon of any kind be absorbed by a free electron? (Hint: consider conservation of momentum and energy.)

3

X-rays of wavelength 70pm are scattered offa carbon target as shown in the figure. The resulting x-rays detected are plotted by their wavelength and relative signal intensity.

Explain why there are two peaks in each of the spectra.

Problem solving questions

4

Which is true? The Compton Effect is evidence that photons carry:

(a) energy and charge

(b) energy and momentum

(c) energy and mass

5

Compton scattering of photons is described by Δλ = (h/mec)(1 - cosφ). This shift is easy to observe with X - rays, but not with visible light. Why might this be the case?

6

X-rays of energy 40 keV are incident on a block of carbon and undergo Compton scattering.

(a) Calculate the wavelength of the incident X-rays

(b) What is the maximum possible Compton shift, and for what angle does this occur?

(c) Compton scattering in carbon occurs from both free electrons and integrated charge of the atom. How would you distinguish X-rays scattered by the atom from those scattered by free electrons?

7

A beam of x-rays of wavelength 30 pm is directed onto an aluminium target as shown in figure (a), and the distribution of the scattered X-rays is shown in diagram (b) below.

If a beam of electrons of a suitable energy was used instead of X-rays, the distribution of the scattered electrons will resemble diagram (c). As can be seen, the two diffraction images have almost identical spacings.

a) What conclusion can be drawn from the similarity of the scattered X-ray and electron images?

b) What is the momentum  of the electrons used in the electron measurement?

c) What is the energy of the electron beam?

8

X-rays of unknown wavelength are scattered from a crystal. The spacing between each atom in the crystal is 0.30 nm. A detector is used to measure the intensity of scattered X-rays at various angles, and a maximum is observed at an angle of  θ = 30° .

a) Show that the path-difference between the scattered x-rays from  adjacent layers is given by 2dsinθ .

b) Calculate at least two possible values of the wavelengths ofthe scattered X-rays.

9

Inside an x-ray machine, electrons are accelerated into a Tungsten target using a 40 kV potential difference, to produce x-rays. Calculate the shortest possible wavelength that can be emitted from its target.

Past exam questions

10

A beam of low energy electrons is directed onto a crystal target, to study the angular dependence of the scattered electrons. This is similar to the setup used by Davisson and Germer where they found at particular angles there was a peak in the intensity of the scattered electron beam.

At an accelerating potential difference of 55 V, a definite peak in the scattered electrons is found at an angle of θ = 65°.

a)   Briefly explain the scattering process that leads to the formation of peaks in the intensity of scattered electrons. Include in your answer a reference to the property of electrons that is relevant.

b)   Show that the momentum of the incident electrons is approximately 4.0 × 10一24 kg. ms一1

c)   With the aid of Bragg’s law (2d sin θ = nλ) and assuming n = 1, determine the lattice spacing in the crystal.

11

a) The diagram shows a simple electron gun setup for an electron microscope. It consists of a visible laser that is used to release electrons from a polished metal surface (A). These electrons are then accelerated from rest by a potential difference of 600 V between plates A and B.  The geometry is such that the energetic electrons pass horizontally through a  1 mm hole in B and reach a phosphor screen C, where a bright spot of about 1 mm in diameter can be observed. The entire apparatus is operated under vacuum conditions.

i)  Identify and explain the physical process by which the laser releases electrons from the metal surface.

ii)  Estimate the velocity of the electrons as they pass through the hole at B.

iii) Calculate the de Broglie wavelength of the electrons.

In an attempt to reduce the spot size at C, the hole in the plate B is gradually made smaller and smaller. It is now almost as small as the de Broglie wavelength of the electrons.

b)   Comment on whether this procedure will achieve the desired goal. Justify your answer.

12

X-rays of energy 56 keV (wavelength 22 pm) are Compton scattered from a carbon target, and the scattered x-rays are detected at an angle of 85° to the incident beam.

(a)  Calculate the wavelength for x-rays that are Compton scattered by the outer-shell (essentially “free”) electrons of the carbon atoms.

The carbon target is replaced with a much heavier target made of lead.

(b)  What now is the wavelength for x-rays that are Compton scattered by the outer shell electrons of the lead atoms?