# Worksheet: Electron Diffraction and Microscopy

In this worksheet, we will practice describing electron beam diffraction, how it is used in electron microscopy, and how other forms of electron microscopy compare to it.

Q1:

A rectangular section of an electrostatic lens in an electron microscope is shown in the diagram. The electric potential increases along the length of the lens; the potential is greater than the potential . An electron moves parallel to the axis of the lens. Which of the paths I, II, and III shown does the electron move along? • AII
• BIV
• CIII
• DI
• ENone of these paths

Q2:

A beam of electrons passes through a crystal. A diffraction pattern of concentric rings is formed on a screen behind the crystal that records the positions of electrons that arrive at it, as shown in the diagram. The intensity of the rings is plotted against the radial distance from the center of the pattern. The resulting intensity distribution is shown three times, each time compared to another intensity distribution that is shown below it. Which of the intensity distributions would result from decreasing the velocity of the electrons in the beam?

• AII
• BI
• CNone of these distributions
• DIII

Which of the intensity distributions would result from decreasing the charge density of the electron beam while not changing the velocity of the electrons in the beam?

• AIII
• BI
• CII
• DNone of these distributions

Q3:

Which of the following correctly states the advantage of using electrons to produce images of very small objects compared to using electromagnetic waves?

• AElectrons are reflected from objects more strongly than electromagnetic waves.
• BElectrons can penetrate deeper into objects than electromagnetic waves.
• CA beam of electrons will in no way affect an object that it produces an image of, so it produces a more valid image than the ones that can be produced by electromagnetic waves.
• DElectrons can easily be accelerated to velocities at which they have wavelengths much shorter than those of electromagnetic waves with wavelengths that are useful in forming images.

Q4:

Which of the following are correct statements about the similarities between transmission electron microscopes and scanning tunneling electron microscopes?

• ABoth types of microscopes use electrons emitted from objects to form images.
• BBoth types of microscopes use electric, magnetic, or electromagnetic lenses to shape electron beams.
• CBoth types of microscopes use electrons to produce images.
• DBoth types of microscopes use electron diffraction to form images.
• EBoth types of microscopes require an electron beam emitter.

Q5:

A particle accelerator accelerates electrons through a potential difference , as shown in the diagram. Find the wavelength of electrons as they exit the accelerator. Use a value of C for the charge of electrons, a value of kg for the mass of electrons, and a value of J⋅s for the Planck constant. • A m
• B m
• C m
• D m
• E m

Q6:

Which of the following statements about scanning electron microscopes, but not other types of electron microscopes, is true?

• AElectrons scattered from the imaged object are used in image formation.
• BThe internal structure of objects can be imaged.
• CElectron diffraction is used in image formation.
• DElectrons that pass from the imaged object to the microscope by quantum tunneling are used in image formation.
• EElectric, magnetic, and electromagnetic lenses are parts of the microscope.

Q7:

Which of the following statements about scanning tunneling electron microscopes, but not other types of electron microscopes, is true?

• AElectrons that pass from the imaged object to the microscope by quantum tunneling are used in image formation.
• BElectrons scattered from the imaged object are used in image formation.
• CElectric, magnetic, and electromagnetic lenses are parts of the microscope.
• DElectron diffraction is used in image formation.
• EThe internal structure of objects can be imaged.

Q8:

A particle accelerator accelerates electrons through the potential difference between and , as shown in the diagram. The smallest value of the velocity of the electron is at . Which waveform corresponds to that of an electron moving across the accelerator? • A • B • C • D • E Q9:

A rectangular section of a cylindrical electrostatic lens in an electron microscope is shown in the diagram. The electric potential increases along the length of the lens; the potential is greater than the potential . An electron that is equidistant from the sides of the lens moves parallel to the axis of the lens. Which of the paths I, II, and III shown does the electron move along? • AIII
• BII
• CI
• DNone of these paths

Q10:

A circular section of a magnetic lens in an electron microscope is shown in the diagram. Four electrons, A, B, C, and D, travel perpendicularly to the plane of the lens section, toward the viewer. In which of the directions I, II, III, and IV does electron A accelerate due to the magnetic force acting on it?

• AII
• BIII
• CI
• DIV
• ENone of these directions

In which of the directions I, II, III, and IV does electron B accelerate due to the magnetic force acting on it?

• AII
• BIII
• CI
• DIV
• ENone of these directions

In which of the directions I, II, III, and IV does electron C accelerate due to the magnetic force acting on it?

• AIII
• BI
• CII
• DIV
• ENone of these directions

In which of the directions I, II, III, and IV does electron D accelerate due to the magnetic force acting on it?

• AIV
• BII
• CI
• DIII
• ENone of these directions

Q11:

A particle accelerator accelerates electrons through a potential difference of V, as shown in the diagram. The wavelength of electrons as they exit the accelerator is m. Find . Use a value of for the size of the charge of electrons, a value of kg for the mass of electrons, and a value of J⋅s for the Planck constant. • A3.7 V
• B12 V
• C7.4 V
• D28 V
• E14 V

Q12:

A beam of electrons that have a velocity, , passes through a crystal in which the atoms have an average separation of , as shown in the diagram. A diffraction pattern of concentric rings is formed on a screen, recording the positions of electrons that arrive at it, behind the crystal. Maximum diffraction occurs when the beam is incident normal to the crystal and then a single spot is observed. For maximum diffraction, . Calculate in the case of maximum diffraction. Use a value of kg for the mass of the electrons and use a value of J⋅s for the Planck constant. • A m/s
• B m/s
• C m/s
• D m/s
• E m/s

Q13:

A beam of electrons that have a velocity of m/s passes through a crystalline material. The diffraction of the electrons produces a pattern containing a single spot. A single spot diffraction pattern occurs when the electrons are normally incident on the plane of the crystal lattice and the separation of the planes of the crystal lattice is half the wavelength of the electrons. Find . Use a value of kg for the mass of the electrons and a value of J⋅s for the Planck constant.

• A m
• B m
• C m
• D m
• E m

Q14:

The diagram shows some parts of an electron beam that is passing through a crystal lattice. The lattice has parallel planes separated by a perpendicular distance . Some of the electrons in the beam are scattered by the atoms of the lattice. The electrons all have a wavelength . Each of the blue dotted lines in the diagram corresponds to a separate wave. The waves at points and are in phase with each other, and the waves at points and are in phase with each other. Lines and are parallel. Which of the following correctly describes the length of the path traveled by electrons between point and point ?

• AThe length is equal to .
• BThe length is equal to , where is an integer.
• CThe length is equal to , where is an integer.
• DThe length is equal to , where is an integer.
• EThe length is equal to , where is an integer.

Which of the following correctly describes the relationship between angles and ?

• A
• B
• C