QuestionIn an electron diffraction tube, electrons are accelerated from rest through a potential difference of 150 V and then pass through a thin film of graphite. The spacing between the layers of atoms in graphite is about 1 × 10-10 m.(a) Calculate the kinetic energy of each electron. (1)
(b) Show that the momentum of each electron is about 6.6 × 10-24 kg m s-1. (2)
(c) Calculate the de Broglie wavelength of the electrons and explain why they are diffracted by the graphite. (3)Mass of electron = 9.11 × 10-31 kgAnswer(a) Ek = eV = 1.60 × 10-19 × 150 = 2.40 × 10-17 J (1)(b) Ek = p2 / 2m, so p = √(2mEk) (1)p = √(2 × 9.11 × 10-31 × 2.40 × 10-17) = 6.61 × 10-24 kg m s-1
(1)(c) λ = h / p = 6.63 × 10-34 ÷ 6.61 × 10-24 = 1.00 × 10-10 m (1)This wavelength is about the same as the spacing between the layers of atoms in graphite, (1) so the gaps act like a diffraction grating and the electrons are noticeably diffracted. (1)Examiner tips- In a "show that" question, give your answer to more significant figures than the value quoted (6.61, not 6.6).
- Do not use the photon equations E = hf or λ = hc / E for electrons. Use λ = h / p.
- At 600 V the momentum would double and the wavelength would halve, so the rings would be smaller.
(b) Show that the momentum of each electron is about 6.6 × 10-24 kg m s-1. (2)
(c) Calculate the de Broglie wavelength of the electrons and explain why they are diffracted by the graphite. (3)Mass of electron = 9.11 × 10-31 kgAnswer(a) Ek = eV = 1.60 × 10-19 × 150 = 2.40 × 10-17 J (1)(b) Ek = p2 / 2m, so p = √(2mEk) (1)
(1)(c) λ = h / p = 6.63 × 10-34 ÷ 6.61 × 10-24 = 1.00 × 10-10 m (1)This wavelength is about the same as the spacing between the layers of atoms in graphite, (1) so the gaps act like a diffraction grating and the electrons are noticeably diffracted. (1)Examiner tips- In a "show that" question, give your answer to more significant figures than the value quoted (6.61, not 6.6).
- Do not use the photon equations E = hf or λ = hc / E for electrons. Use λ = h / p.
- At 600 V the momentum would double and the wavelength would halve, so the rings would be smaller.