Question 7
7
Electrons, travelling at speed v in a vacuum, are incident on a very thin carbon film, as illustrated in Fig. 7.1. The emergent electrons are incident on a fluorescent screen. A series of concentric rings is observed on the screen.
structured9 marks
Question 7(a)
7(a)
Suggest why the observed rings provide evidence for the wave nature of particles.
Mediumstructured2 marks
Answer
either if light passes through suitable film / cork dust etc. diffraction occurs and similar pattern observed or concentric circles are evidence of diffraction diffraction is a wave property
Question 7(b)
7(b)
The initial speed of the electrons is increased. State and explain the effect, if any, on the radii of the rings observed on the screen.
Mediumstructured3 marks
Answer
(speed increases so) momentum increases \(\lambda=h / p\) so \(\lambda\) decreases hence radii decrease (special case: wavelength decreases so radii decreases - scores 1/3) or (speed increases so) energy increases \(\lambda=h / \sqrt{ }(2 E m)\) so \(\lambda\) decreases hence radii decrease
Question 7(c)
7(c)
A proton and an electron are each accelerated from rest through the same potential difference. Determine the ratio \(\frac{\text { de Broglie wavelength of the proton }}{\text { de Broglie wavelength of the electron }}\). ratio =
Hardstructured4 marks
Answer
electron and proton have same (kinetic) energy either \(E=p^{2} / 2 m\) or \(p=\sqrt{ }(2 E m)\) C1 ratio \(=p_{\mathrm{e}} / p_{\mathrm{p}}=\sqrt{ }\left(m_{\mathrm{e}} / m_{\mathrm{p}}\right)\) \(=\sqrt{ }\left\{\left(9.1 \times 10^{-31}\right) /\left(1.67 \times 10^{-27}\right)\right\}\) \(=2.3 \times 10^{-2}\)
Question 7
7
Electrons, travelling at speed v in a vacuum, are incident on a very thin carbon film, as illustrated in Fig. 7.1. The emergent electrons are incident on a fluorescent screen. A series of concentric rings is observed on the screen.
structured9 marks
Question 7(a)
7(a)
Suggest why the observed rings provide evidence for the wave nature of particles.
Mediumstructured2 marks
Answer
either if light passes through suitable film / cork dust etc. diffraction occurs and similar pattern observed or concentric circles are evidence of diffraction diffraction is a wave property M1 A1 (M1) (A1) [2]
Question 7(b)
7(b)
The initial speed of the electrons is increased. State and explain the effect, if any, on the radii of the rings observed on the screen.
Mediumstructured3 marks
Answer
(speed increases so) momentum increases M1 \(\lambda=h / p\) so \(\lambda\) decreases A1 [3] (special case: wavelength decreases so radii decreases - scores 1/3) or (B1) (M1) (A1)
Question 7(c)
7(c)
A proton and an electron are each accelerated from rest through the same potential difference. Determine the ratio \(\frac{\text { de Broglie wavelength of the proton }}{\text { de Broglie wavelength of the electron }}\). ratio =
Hardstructured4 marks
Answer
electron and proton have same (kinetic) energy either \(E=p^{2 / 2 m\) or \(p=\sqrt{ }(2 E m)\) ratio \(=p_{\mathrm{e}} / p_{\mathrm{p}}=\sqrt{ }\left(m_{\mathrm{e}} / m_{\mathrm{p}}\right)\) \(=\sqrt{ }\left\{\left(9.1 \times 10^{-31}\right) /\left(1.67 \times 10^{-27}\right)\right\}\) \(=2.3 \times 10^{-2}\)} C1 C1 C1 A1 [4]
Question 8
8
\(8 \mathrm{~A} \pi^{0}\) meson is a sub-atomic particle. A stationary \(\pi^{0}\) meson, which has mass \(2.4 \times 10^{-28} \mathrm{~kg}\), decays to form two \(\gamma\)-ray photons. The nuclear equation for this decay is
structured2 marks
Question 8(b)
8(b)
Determine, for each \(\gamma\)-ray photon,
structured2 marks
Question 8(b)(ii)
8(b)(ii)
the wavelength, wavelength = m
Mediumstructured2 marks
Answer
\(E=h c / \lambda\) \(\lambda=\left(6.63 \times 10^{-34} \times 3.0 \times 10^{8}\right) /\left(1.08 \times 10^{-11}\right) \quad \mathrm{C} 1\)
Question 7
7
9 marks
Question 7(a)
7(a)
State what is meant by the de Broglie wavelength.
Easystructured1 marks
Answer
wavelength associated with a moving particle B1
Question 7(b)
7(b)
Fig. 7.1 shows a glass tube in which electrons are accelerated through a high p.d. to form a beam that is incident on a thin graphite crystal. After passing through the graphite crystal, the electrons reach the fluorescent screen. The screen glows where the electrons strike it. Fig. 7.2 shows the fluorescent screen viewed end-on, from the right-hand side of Fig. 7.1.
structured3 marks
Question 7(b)(i)
7(b)(i)
State the name of the phenomenon demonstrated by the pattern shown in Fig. 7.2.
Easystructured1 marks
Answer
(electron) diffraction B1
Question 7(b)(ii)
7(b)(ii)
Explain what can be concluded from the pattern in Fig. 7.2 about the nature of electrons.
Mediumstructured2 marks
Answer
beam spreads out indicating diffraction or light and dark regions indicate an interference pattern B1 electron beam is behaving as a wave B1
Question 7(c)
7(c)
The electrons in (b) are now accelerated through a greater potential difference between the cathode and the anode.
structured5 marks
Question 7(c)(i)
7(c)(i)
On Fig. 7.3, sketch the pattern that is now seen on the fluorescent screen in Fig. 7.1.
Mediumstructured2 marks
Answer
central blob and concentric rings B1 rings closer together (than previously) B1
Question 7(c)(ii)
7(c)(ii)
Explain, with reference to de Broglie wavelength, the change in the pattern on the fluorescent screen.
Mediumstructured3 marks
Answer
(greater p.d. so) electrons to have greater momentum B1 greater momentum so decrease in (de Broglie) wavelength B1 lower (de Broglie) wavelength (for same grating spacing in crystal) causes: smaller diffraction angle or smaller angle of intensity maxima (for each order) or decrease in fringe spacing in diffraction pattern B1