VCE Physics - Diffraction Patterns 1 - waves and particles

Which one of the following is closest to the de Broglie wavelength of a 663 kg motor car moving at 10 m s⁻¹?

_{VCAA 2021}

• 10⁻³⁷ m

• 10⁻³⁶ m

• 10⁻³⁵ m

• 10⁻³⁴ m

Answer explanation

Use p = Use p=h/λ

       λ = h/p

= h/mv

= 6.63 × 10⁻³⁴ /(663 × 10)

       λ = 1.00 × 10^-37 m

When a beam of X-rays of a single wavelength passes through a metal foil, a pattern of rings is detected by photographic film.

How do the X-rays produce this pattern of rings?

(Select two options)

_{VCAA 2000}

• the ring pattern was an interference/diffraction pattern formed by the X-rays passing through the metal

• the rings themselves represented positions of destructive interference

• the rings themselves represented positions of constructive interference

• the pattern occurs because the wavelength of the X-rays is half that of the atomic spacing of the metal crystal.

• the interference pattern occurs because the metal foil atoms block transverse waves in most directions

A parallel beam of red light is incident on a single slit. A photographic film placed several metre away records the resultant diffraction pattern. The diagram indicates the intensity of light recorded on the film.

The diffraction pattern can be explained if one assumes that

_{VCAA 1971}

• the two edges of the slit are acting as two point sources in phase

• the slit is acting as a single point source.

• the slit is acting as two point sources half a cycle out of phase

• the slit is acting as a row of point sources in phase

Answer explanation

The local minima are from destructive interference between two pairs of points. To determine their position, we model the slit as a series of adjacent point sources.

When light of single wavelength passes through two close, narrow slits a pattern of light and dark bands is observed on a screen that is about 2 metres from the slits. The experimental arrangement is illustrated

Select two options that explain whether the particle model or the wave model for light best explains the observations of this experiment.

_{VCAA 1997}

• Waves from the two slits will interfere with each other to form the dark and light bands. Light bands are constructive interference.

• Photons of light that are in phase will pass through the slits and collide to form dark bands

• Bright bands are formed when the path difference from each slit is a whole multiple of the wavelength

• Inteference is evidence of the particle nature of light

Answer explanation

This interference pattern is best explained from the wave model. Waves from the two point sources (the slits) will interfere with each other at the screen. You will get bands of constructive and destructive interference. A path difference of λ/2, 3λ/2, 5λ/2 etc. will produce nodal lines. (A dark band is due to destructive interference). The bright central band will always be a region where constructive interference occurs

The figure shows both an X-ray diffraction pattern (the upper half of the figure), and a diffraction pattern obtained using electrons (the lower half of the figure). Both were obtained with an aluminium foil.

The X-ray photons had an energy of 2.38 × 10^-16 J, and a momentum of 7.94 × 10^-25 kg m s^-1.

What was the wavelength of the X-rays used in this experiment?

_{VCAA 1995}

• 1.2 x 10⁹ m

• 5.2 x 10¹⁰ m

• 8.4 × 10^-10 nm

• 8.4 × 10^-10 m

Answer explanation

From λ = h/p

We get

 λ = h/p

= (6.63x10^-34)/(7.94x10^-25)

= 8.4 × 10^-10 m

The figure shows both an X-ray diffraction pattern (the upper half of the figure), and a diffraction pattern obtained using electrons (the lower half of the figure). Both were obtained with an aluminium foil.

The electron and X-ray diffraction patterns have the same spacing between rings. Did the electrons which produced the pattern have the same energy as the X-ray photons used, or the same momentum as the X-ray photons? (select two options)

_{VCAA 1995}

• The wavelength is the same, so the momentum will be the same

• The wavelength is the same, so the energy will be the same

• The same spacing means the energy is the same

• The same spacing means the wavelength is the same

Answer explanation

The same diffraction pattern implies that the wavelength is the same.

The same wavelength implies that the momentum is the same.

The diffraction patterns for X-rays and electrons through thin polycrystalline aluminium foil have been combined in the diagram, which shows an electron diffraction pattern on the left and an X-ray diffraction pattern on the right. The images are to the same scale.

The X-rays have a photon energy of 8000 eV.

Calculate the wavelength of the electrons in nanometres

_{2018 VCAA}

• 0.155 nm

• 1.55 x 10^-10 m

• 2.48 x 10^-20 nm

• 0.31 nm

Answer explanation

The X-rays have photons with energy of 8000 eV,

Use E =  to find the wavelength of the X-rays. The electrons will have the same wavelength as they have the same diffraction pattern.

For an X-ray, E =  hc/λ

 λ =  hc/E

=  4.14 x 10^-15 x 3 x 10⁸ /8000

= 1.55 × 10^-10 m

λ = 0.155 nm

The answer in nm as requested.

The diffraction patterns for X-rays and electrons through thin polycrystalline aluminium foil have been combined in the diagram, which shows an electron diffraction pattern on the left and an X-ray diffraction pattern on the right. The images are to the same scale.

The X-rays have a photon energy of 8000 eV.

Calculate the kinetic energy of the electrons in joules

_{2018 VCAA}

• 1.6 x 10^-27 J

• 1.5 x 10¹⁶ J

• 2 x 10⁶ J

• 1 × 10^-17 J

Answer explanation

Combine E=p²/2m and p=h/λ to get:

E=h² /2mλ²

= (6.63x10^-34)²/(2x9.1x10^-31x(1.55

x10^-10)²)

= 1x10^-17 J

The other options provided were produced when one or both of the squares were omitted.

Students are comparing the diffraction patterns produced by electrons and X-rays, in which the same spacing of bands is observed in the patterns. Note that both patterns shown are to the same scale

Why electrons can produce the same spacing of bands in a diffraction pattern as X-rays? Select multiple answers

_{2019 VCAA}

• Moving electrons have a de Broglie wavelength

• the wavelength of the electrons needs to be the same as that of the X-rays.

• the energy of the electrons needs to be the same as that of the X-rays.

• diffraction is dependent on wavelength

• diffraction is dependent on photon energy

Answer explanation

To get the same spacing of the bands the wavelength of the electrons needs to be the same as that of the X-rays.

The pattern demonstrates that electrons exhibit wave like properties and have a wavelength.

Which of the statements best explains why it is possible to compare X-ray and electron diffraction patterns?

_{VCAA 2002}

• X-rays can exhibit particle-like properties

• Electrons can exhibit wave-like properties

• Electrons are a form of high energy X-rays

• Both electrons and X-rays ionise matter

Answer explanation

The diffraction pattern is due to the wavelike properties of each