Q188 · Practice questionComplex familiar7 marks
QUESTION 188 (7 marks)
Two observations are made: (1) monochromatic light passing through two narrow slits forms alternating bright and dark bands; (2) a metal shows a threshold frequency for immediate photoelectron emission, and no emission below threshold in the one-photon regime even at higher intensity.
a)[3 marks]
Explain how observation 1 supports the wave model of light.
b)[3 marks]
Explain how observation 2 supports the photon model rather than an unquantised energy-transfer model.
c)[1 mark]
State what the two observations imply about a complete description of light.
WORKED SOLUTION
7 marksPractice marking scheme
ANSWER
(a) Overlapping coherent waves interfere, giving reinforcement and cancellation according to path difference. (b) An electron absorbs one photon of energy hf, which must meet the work function; more sub-threshold photons do not increase energy per photon. (c) Light exhibits wave–particle duality: both types of evidence must be accounted for.
Worked solution
(a) Light from the two slits overlaps at the screen. Where the path difference is an integer multiple of wavelength, waves arrive in phase and their amplitudes reinforce, giving a bright band. Where it is a half-integer multiple, opposite phases cancel and give a dark band.
(b) In the photon model an electron receives energy from a single photon. Emission requires , so . Below threshold, increasing intensity increases photon number but leaves too small. At sufficient frequency, a single interaction can cause immediate emission without accumulating energy over a long exposure.
(c) The wave description explains the interference evidence and the photon description explains the threshold evidence. A complete model must accommodate both.
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: Identify superposition or interference of waves from the slits.
Part a: Explain the bright bands using in-phase reinforcement.
Part a: Explain the dark bands using opposite-phase cancellation.
Part b: Describe quantised photon energy transferred to an electron.
Part b: Explain the threshold in terms of the work function.
Part b: Explain why increased sub-threshold intensity does not cause one-photon emission.
Part c: State wave–particle duality linked to the two observations.
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