Diffraction and the wave nature of electrons

Plane water waves in a ripple tank pass through a gap in a barrier. The waves spread out only slightly beyond the gap.
Which change would make the waves spread out more?

Huygens' construction is used to predict the position of a wavefront a short time later.
Which statement describes the construction?

A diffraction grating has 250 lines per mm.
What is the spacing between adjacent slits?

In a school laboratory, microwaves of wavelength 2.8 cm from a transmitter pass through a gap of width 3.0 cm between two metal plates. A receiver is moved around the far side of the plates. c = 3.00 × 10⁸ m s⁻¹.

Violet light of wavelength 405 nm from a laser is incident normally on a diffraction grating with 500 lines per mm.

An electron travels at a speed of 3.2 × 10⁶ m s⁻¹. e = 1.60 × 10⁻¹⁹ C, m_e = 9.11 × 10⁻³¹ kg, h = 6.63 × 10⁻³⁴ J s.

Figure 1 shows four ripple tank set-ups drawn to scale on a grid of 1.0 cm squares. In each one, straight wavefronts travel towards a gap in a barrier.
In which set-up will the waves spread out most after passing through the gap?

Light of wavelength 589 nm is incident normally on a diffraction grating. Figure 1 shows the beams travelling from the grating to the central maximum and to the two first-order maxima.
How many lines per mm does the grating have?

Figure 1 shows the patterns produced when a beam of X-rays, and then a beam of electrons, pass through the same thin metal foil. The two patterns are drawn to the same scale.
Which conclusion can be drawn from the figure?

Figure 1 shows a plan view of straight water waves in a ripple tank travelling towards a gap in a barrier. The bar that makes the waves vibrates with a frequency of 12 Hz.

Figure 1 is a plan view of a room and a corridor separated by a wall with a doorway. A loudspeaker S in the room emits a steady note. A listener stands at L in the corridor. The speed of sound in air is 340 m s⁻¹.

Figure 1 shows an electron diffraction tube and a face-on view of its screen. e = 1.60 × 10⁻¹⁹ C, m_e = 9.11 × 10⁻³¹ kg, h = 6.63 × 10⁻³⁴ J s.

Blue light of wavelength 470 nm is incident normally on a grating with 600 lines per mm.
What is the angle between the second-order maximum and the straight-through direction?

Red light of wavelength 650 nm is incident normally on a grating with 520 lines per mm.
What is the total number of maxima produced, including the central maximum?

A student shines a laser normally onto a grating with 100 lines per mm. On a screen 2.40 m from the grating, the distance between the two first-order maxima is 0.310 m.
What is the wavelength of the laser light?

Which observation provides evidence that electrons have wave properties?

A proton moves at a speed of 4.4 × 10⁵ m s⁻¹. m_p = 1.67 × 10⁻²⁷ kg, h = 6.63 × 10⁻³⁴ J s.
What is the de Broglie wavelength of the proton?

A mercury lamp emits a yellow line of wavelength 577 nm. Light from the lamp falls normally on a diffraction grating, and the first-order maximum for this line is observed at an angle of 20.3° to the straight-through direction.

A student uses a grating with 250 lines per mm to find the wavelength of a red laser. The screen is 0.850 m from the grating. She measures the distance x from the central maximum to the maxima of orders 1, 2 and 3 on one side:
n = 1: x = 0.140 m; n = 2: x = 0.292 m; n = 3: x = 0.475 m.

In an electron diffraction tube, electrons are accelerated through a potential difference of a few kilovolts and then pass through a very thin film of graphite before hitting a fluorescent screen.

In an electron gun, electrons are accelerated from rest through a potential difference of 1800 V. e = 1.60 × 10⁻¹⁹ C, m_e = 9.11 × 10⁻³¹ kg, h = 6.63 × 10⁻³⁴ J s.

Figure 1 shows Huygens' construction for a straight wavefront in a gap in a barrier. Secondary wavelets (dashed) have been drawn from points on the wavefront in the gap. In each of the panels P, Q, R and S, a different thick line has been drawn as the new wavefront.
In which panel is the new wavefront drawn correctly?

A student shines a laser of wavelength 600 nm normally onto a diffraction grating and measures the angle θ of the maxima of orders n = 1 to 4. Figure 1 shows her graph of sin θ against n.
How many lines per mm does the grating have?

Figure 1 shows how sin θ for the first-order maximum produced by a diffraction grating depends on the wavelength λ of light incident normally on the grating.
Light of wavelength 700 nm is incident normally on the grating. What is the highest order of maximum that can be observed?

Laser light is incident normally on a grating with 150 lines per mm. A screen is placed parallel to the grating, 1.50 m from it. Figure 1 shows the spots on the screen, with a metre rule placed alongside.
What is the wavelength of the laser light?

Figure 1 shows an electron gun. Electrons leave the cathode with negligible speed and are accelerated to the anode. The potentials of the cathode and the anode relative to earth are shown. e = 1.60 × 10⁻¹⁹ C, m_e = 9.11 × 10⁻³¹ kg, h = 6.63 × 10⁻³⁴ J s.
What is the de Broglie wavelength of the electrons that reach the graphite film?

A diffraction grating with 450 lines per mm is mounted on a spectrometer. Light from a lamp that emits two visible spectral lines, X and Y, falls normally on the grating. Figure 1 shows the angle scale with the readings for the straight-through position and for the first-order images of X and Y on both sides.

Figure 1 shows part of a diffraction grating seen through a microscope. Light of wavelength 532 nm from a laser is incident normally on the grating.

To measure the wavelength of light from a laser, a student uses a grating with 300 lines per mm. She measures the distance x on a screen from the central maximum to one first-order maximum, for different grating-to-screen distances D. Figure 1 shows her results and the best-fit line.

Figure 1 shows how the kinetic energy gained by a particle that starts from rest depends on the accelerating potential difference V, for an electron and for an α-particle. m_e = 9.11 × 10⁻³¹ kg, m_α = 6.64 × 10⁻²⁷ kg, h = 6.63 × 10⁻³⁴ J s, 1 eV = 1.60 × 10⁻¹⁹ J.

Electrons accelerated from rest through a potential difference V have a de Broglie wavelength λ. Relativistic effects are negligible.
The potential difference is increased to 4V. What is the new de Broglie wavelength?

Electrons are to be accelerated from rest so that their de Broglie wavelength is 1.5 × 10⁻¹⁰ m. e = 1.60 × 10⁻¹⁹ C, m_e = 9.11 × 10⁻³¹ kg, h = 6.63 × 10⁻³⁴ J s.
What accelerating potential difference is needed?

A student is given a diffraction grating marked with its number of lines per mm, a laser, a large screen, a metre rule and a tape measure.

A student uses an electron diffraction tube to test the de Broglie equation. For each accelerating potential difference V she measures the radius r of the inner ring on the screen:
V = 2.0 kV: r = 16.9 mm; V = 3.0 kV: r = 13.7 mm; V = 4.0 kV: r = 11.9 mm; V = 5.0 kV: r = 10.6 mm.
For these small angles, r is proportional to the de Broglie wavelength λ of the electrons.

Slow-moving neutrons are used to study crystal structures. A beam of neutrons is to have a de Broglie wavelength of 1.8 × 10⁻¹⁰ m. m_n = 1.67 × 10⁻²⁷ kg, m_e = 9.11 × 10⁻³¹ kg, h = 6.63 × 10⁻³⁴ J s, 1 eV = 1.60 × 10⁻¹⁹ J.

Figure 1 shows two electron diffraction patterns, X and Y, produced by the same graphite film in the same tube. Pattern X was obtained with an accelerating potential difference of 3.0 kV. The radius of each ring is proportional to the de Broglie wavelength of the electrons. Relativistic effects are negligible.
What accelerating potential difference was used for pattern Y?

Figure 1 shows how the de Broglie wavelength λ depends on 1/v, where v is the speed, for two particles X and Y. Relativistic effects are negligible.
What is the value of (mass of X) ÷ (mass of Y)?

A student uses one laser and six different diffraction gratings. For each grating she notes the number of lines per mm, N, and measures the angle θ of the first-order maximum. Figure 1 shows a graph of sin θ against N with the best-fit line.

Electrons are accelerated from rest through different potential differences V, and their de Broglie wavelength λ is found from the ring pattern they produce with a graphite film. Theory gives λ = h/√(2m_eeV). Figure 1 shows a graph of λ against 1/√V with the best-fit line. e = 1.60 × 10⁻¹⁹ C, m_e = 9.11 × 10⁻³¹ kg.

An electron starts from rest at the cathode of an electron gun and is accelerated uniformly to the anode, then continues at constant speed. Figure 1 is its velocity–time graph. e = 1.60 × 10⁻¹⁹ C, m_e = 9.11 × 10⁻³¹ kg, h = 6.63 × 10⁻³⁴ J s.