Quantum theory — Question 129

Original QCE Vault practice · 9 marks

Q129 · Practice questionComplex unfamiliar9 marks

QUESTION 129 (9 marks)

A photoelectric experiment gives the following stopping potentials:

\frac{f}{10^{14} Hz} = 5.5, 6.5, 7.5, 8.5

and

\frac{V_s}{V} = 0.18, 0.59, 1.01, 1.43

. Treat the trend as linear.

Original diagram for Physics Paper 1 question 24

Determine the

\frac{\text{gradient} dV_s}{\mathrm{d}f}

and use it to estimate Planck’s constant.

[3 marks]

Estimate the threshold frequency and work function.

[3 marks]

Explain how the data support the photon model and identify one experimental limitation.

[3 marks]

Question linkSyllabus coverage

WORKED SOLUTION

Practice marking scheme

9 marks

ANSWER

The approximately linear

V_s

–

f

relation and non-zero threshold agree with

eV_s=hf-\phi

, showing energy is delivered in photons. A limitation could be contact-potential uncertainty, surface contamination, finite meter resolution or scatter in stopping-potential determination.

Worked solution

Part (a): Using endpoints,

\text{gradient}=\frac{1.43-0.18}{(8.5-5.5)\times10^{14}}=4.17\times10^{-15}\,\mathrm{V}\,\mathrm{s}

. Since

eV_s=hf-\phi , h=e(\text{gradient})=(1.602\times10^{-19})(4.17\times10^{-15})=6.68\times10^{-34}\,\mathrm{J}\,\mathrm{s}

Part (b): Using

V_s=mf+c

c=0.18-(4.17\times10^{-15})(5.5\times10^{14})=-2.11\,\mathrm{V}

. Threshold

f0=-\frac{c}{m}=5.06\times10^{14}\,\mathrm{Hz}

. Work function

\phi =hf0\approx 3.38\times10^{-19} J\approx 2.11\,\mathrm{eV}

Part (c): The approximately linear

V_s

–

f

relation and non-zero threshold agree with

eV_s=hf-\phi

, showing energy is delivered in photons. A limitation could be contact-potential uncertainty, surface contamination, finite meter resolution or scatter in stopping-potential determination.

Part (a): completes the requested reasoning and obtains a correct result.

[3 marks]

Part (b): completes the requested reasoning and obtains a correct result.

[3 marks]

Part (c): completes the requested reasoning and obtains a correct result.

[3 marks]

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Quantum theory — Question 129

QUESTION 129 (9 marks)

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