# CIE AS & A Level Physics : 22.3 Wave-particle duality – Exam style question – Paper 4

### Question

(a) State an experimental phenomenon that provides evidence for:

(i) the particulate nature of electromagnetic radiation
……………………………………………………………………………………………………………………. 
(ii) the wave nature of matter.
……………………………………………………………………………………………………………………. 

(b) A particle of matter moves with momentum p.

(i) State the equation that gives the effective wavelength λ of the particle. State the name of any other symbols used.                                                                                                                             

(ii) State the name given to the wavelength of the moving particle.
……………………………………………………………………………………………………………………. 

(c) Electrons are accelerated from rest through a potential difference (p.d.) of 4.8kV.

(i) Show that the final speed of the electrons is 4.1 × 107ms–1.                                                                

(ii) Calculate the effective wavelength of a beam of electrons moving at the speed in (c)(i).
wavelength = …………………………………………….. m                                                                                                                                                                                   [Total: 9]

Ans

(a) (i) photoelectric effect

(a) (ii) electron diffraction

(b) (i) λ = h / p
h is the Planck constant

(b) (ii) de Broglie (wavelength)

(c )(i) ½mv2 = eV
½ × 9.11 × 10–31 × v2 = 1.60 × 10–19 × 4800 so v = 4.1 × 107 m s–1
(c) (ii) λ = h / mv = 6.63 × 10–34 / (9.11 × 10–31 × 4.1 × 107)
= 1.8 × 10–11

### Question

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.

(a) Suggest why the observed rings provide evidence for the wave nature of particles.
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(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.
…………………………………………………………………………………………………………………………
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(c) A proton and an electron are each accelerated from rest through the same potential difference.
Determine the ratio ratio = …………………………………………..

Ans:

(a) either if light passes through suitable film / cork dust etc.
either diffraction occurs and similar pattern observed
or concentric circles are evidence of diffraction
or diffraction is a wave property

(b) (speed increases so) momentum increases
$$λ = h/p$$  so λ decreases
$$λ = h / √(2Em)$$ so λ decreases
either $$E = p^2/ 2m$$ or $$p = √(2Em)$$
ratio $$= p_e / p_p = √(m_e / m_p)$$
ratio $$= \sqrt{\frac{(9.1 × 10^{–31})} { (1.67 × 10^{–27})}$$