Q242 · Practice questionComplex familiar5 marks
QUESTION 242 (5 marks)
An electron beam and a proton beam both have de Broglie wavelength . Both are non-relativistic. Use , and .
a)[2 marks]
Calculate the momentum of a particle in each beam.
b)[2 marks]
Calculate the speed of each particle.
c)[1 mark]
Explain why the common wavelength does not imply a common speed.
WORKED SOLUTION
5 marksPractice marking scheme
ANSWER
(a) Both have . (b) Electron: ; proton: . (c) Wavelength determines momentum; different masses need different speeds for the same momentum.
Worked solution
(a) For either particle, . Equal wavelengths imply equal momentum magnitudes.
(b) Using in the stated non-relativistic regime gives and .
(c) depends on momentum. Since , the lighter electron must move faster than the proton to have the same momentum and wavelength.
Equivalent physically justified methods and consistent equivalent units accepted.
Displayed decimals are model answers; accept appropriate significant figures and consistent rounding from stated constants.
Part a: Apply the de Broglie relation to both beams.
Part a: Calculate the shared momentum magnitude.
Part b: Calculate electron speed from its mass.
Part b: Calculate proton speed from its mass.
Part c: Distinguish momentum from speed and account for the unequal masses.
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