Q187 · Practice questionComplex familiar7 marks
QUESTION 187 (7 marks)
In the Bohr standing-wave model, an electron occupies an orbit of radius . Use and . Treat the electron momentum as nonrelativistic.
a)[2 marks]
Determine the de Broglie wavelength of the electron.
b)[3 marks]
Determine the electron momentum and speed.
c)[2 marks]
Explain why an arbitrary wavelength cannot form a permitted stationary orbit in this model.
WORKED SOLUTION
7 marksPractice marking scheme
ANSWER
(a) . (b) ; . (c) The wave must match itself after one circuit, requiring an integer number of wavelengths.
Worked solution
(a) The circumference contains wavelengths: . Thus .
(b) . With , .
(c) A permitted standing wave is continuous around the closed orbit. Its phase must match after one complete circumference, requiring for an integer . A noninteger number of wavelengths does not close consistently in this model.
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: Use three wavelengths around the orbit.
Part a: Calculate the wavelength.
Part b: Apply the de Broglie momentum relation.
Part b: Calculate momentum.
Part b: Calculate speed from nonrelativistic momentum.
Part c: Explain the matching condition after one circuit.
Part c: Link it to integer quantisation of permitted orbits.
Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.
View the QCAA syllabusHow many marks did you earn?
Compare your working with the guide above.