Diffraction AP Physics 2 MCQ – Exam Style Questions etc.
Diffraction AP Physics 2 MCQ
Unit 14: Waves , Sound , and Physical Optics
Weightage : 15–18%
Exam Style Practice Questions ,Diffraction AP Physics 2 MCQ
Question
The picture above appears in a magazine with a caption indicating that the picture represents electron diffraction by atoms in a crystal. The picture was created by directing a beam of electrons through a thin slice of crystal. The article states that a diffraction pattern like the one shown in the picture can be used to determine the distance between atoms in the crystal used in the experiment.
(a) In a coherent paragraph-length response, explain how electrons can be used to form a diffraction pattern and how the pattern can be used to determine the spacing of atoms in a crystal. Your answer may include a diagram that supports your explanation of the pattern formation.
(b) The article states that x-ray diffraction can also be used to determine crystal spacing. It describes one experiment in which a beam of x-rays with wavelength 8.30 nm was used and another experiment in which a beam of 100 eV electrons was used.
i. Calculate the energy of a photon in the x-ray beam.
ii. Calculate the de Broglie wavelength of an electron in the electron beam.
iii. Will directing the x-ray beam at a crystal with atoms spaced 0.6 nm apart result in the formation of a diffraction pattern? Will directing the electron beam at the same crystal result in the formation of a diffraction pattern? Explain your reasoning in terms of appropriate physics principles.
Answer/Explanation
Ans:
(a) Electrons can have wave properties. The wavelength of the electron can be about the same size as the spacing in the crystal. The evenly spaced pattern of atoms in the crystal acts like slits. The difference in path lengths that produce the constructive and destructive interference pattern can be used to determine the crystal spacing of the atoms in the crystal.
b) i) 
ii) 
iii) The x-ray wavelength is much larger than the crystal spacing and will not be diffracted by the crystal The electron beam wavelength is on the order of the size of the crystal spacing, so a diffraction pattern will appear, or an answer consistent with part (b)i.
Question
You are given the following equipment for use in the optics experiments in parts (a) and (b).
A solid rectangular block made of transparent plastic
A laser that produces a narrow, bright, monochromatic ray of light
A protractor
A meterstick
A diffraction grating of known slit spacing
A white opaque screen
a. Briefly describe the procedure you would use to determine the index of refraction of the plastic. Include a labeled diagram to show the experimental setup. Write down the corresponding equation you would use in your calculation and make sure all the variables in this equation are labeled on your diagram.
b. Since the index of refraction depends on wavelength, you decide you also want to determine the wavelength of your light source. Draw and label a diagram showing the experimental setup. Show the equation(s) you would use in your calculation and identify all the variables in the equation(s). State and justify any assumptions you make.
Answer/Explanation
Ans:
a) Place the laser on the table so that the beam will travel along the white screen placed on the tabletop. Locate the plastic block so that the light enters it at an angle to the normal to the surface of the plastic. Draw a line representing the surface of the block and the incident ray. Mark where the ray exits the block and remove the block. Draw a ray from the exit point back to the normal and incident ray. Measure the angle of incidence and the angle of refraction. Use snell’s law with the index of air=1 to calculate the index for the plastic.
b) Laser diffraction grating screen
Using mλ = d sin θ. Measure x and L to the first bright spot and determine the angle θ with trig. m=1 for the first bright spot, then plug into the equation and solve for the wavelength. The assumption of d<<L is not really an assumption but an experimental parameter to properly use the equation.