Wave/particle duality
Q3. A proton and an electron have the same velocity. The de Boglie wavelength of the electron is 3.2 × 10–8 m.
(a) Calculate,
(i) the velocity of the electron,
λ dB= h/p = h/mv
v = h/mλ dB = 6.63 x 10-34/(9.11 x 10-31 x 3.2 × 10–8)
v = 2.27 × 104 m s–1
v = 2.3 × 104 m s–1
(ii) the de Broglie wavelength of the proton.
λ p = λ e (me/mp)
λ p = 3.2 × 10–8(9.11 x 10-31/1.67 x 10-27)
λ dB = 1.7 × 10-11 m
OR λ dB= h/p = h/mv
λ dB = 6.63 x 10-34/(1.67 x 10-27 x 2.27 × 104)
λ dB = 1.7 × 10-11 m
(4 marks)
(b)
(i) State what kind of experiment would confirm that electrons have a wave-like nature. Experimental details are not required.
Diffraction (experiments)
(ii) State why it is easier to demonstrate the wave properties of electrons than to demonstrate wave properties of protons.
It is easier to obtain a stream of electrons than protons.
(2 marks)
(Total 6 marks)
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