Question(a) Describe one piece of evidence that electrons behave as particles and one piece of evidence that they behave as waves. (2)
(b) A beam of electrons is to be diffracted by a crystal with an atomic spacing of 1.5 × 10-10 m. For strong diffraction, the de Broglie wavelength of the electrons should equal this spacing. Calculate the speed the electrons need. (3)
(c) Calculate the potential difference through which the electrons must be accelerated from rest to reach this speed. (2)Mass of electron = 9.11 × 10-31 kgAnswer(a) Particle: electrons have a fixed mass and charge, and a beam of them is deflected by electric and magnetic fields as individual charged particles. (1) Wave: electrons passing through a thin graphite film produce a diffraction pattern of rings. (1)(b) λ = h / mv, so v = h / mλ (1)v = 6.63 × 10-34 ÷ (9.11 × 10-31 × 1.5 × 10-10) = 4.85 × 106 m s-1
(2)(c) Ek = ½mv2 = 0.5 × 9.11 × 10-31 × (4.85 × 106)2 = 1.07 × 10-17 J (1)V = Ek / e = 1.07 × 10-17 ÷ 1.60 × 10-19 = 67 V
(1)Examiner tips- Wave-particle duality means both models are needed: which behaviour you see depends on the experiment.
- Rearrange before substituting, and put the powers of ten in brackets on your calculator.
- A crystal with smaller spacing would need a shorter wavelength, so faster electrons and a larger accelerating voltage.
(b) A beam of electrons is to be diffracted by a crystal with an atomic spacing of 1.5 × 10-10 m. For strong diffraction, the de Broglie wavelength of the electrons should equal this spacing. Calculate the speed the electrons need. (3)
(c) Calculate the potential difference through which the electrons must be accelerated from rest to reach this speed. (2)Mass of electron = 9.11 × 10-31 kgAnswer(a) Particle: electrons have a fixed mass and charge, and a beam of them is deflected by electric and magnetic fields as individual charged particles. (1) Wave: electrons passing through a thin graphite film produce a diffraction pattern of rings. (1)(b) λ = h / mv, so v = h / mλ (1)
(2)(c) Ek = ½mv2 = 0.5 × 9.11 × 10-31 × (4.85 × 106)2 = 1.07 × 10-17 J (1)
(1)Examiner tips- Wave-particle duality means both models are needed: which behaviour you see depends on the experiment.
- Rearrange before substituting, and put the powers of ten in brackets on your calculator.
- A crystal with smaller spacing would need a shorter wavelength, so faster electrons and a larger accelerating voltage.