Quantum theory — Question 239

Original QCE Vault practice · 6 marks

Q239 · Practice questionComplex unfamiliar6 marks

QUESTION 239 (6 marks)

A photoelectric experiment plots maximum kinetic energy against

1/\lambda

. The exact fitted line passes through A:

(2.00\times10^6\,\mathrm{m^{-1}},1.50\times10^{-19}\,\mathrm J)

and B:

(4.00\times10^6\,\mathrm{m^{-1}},5.50\times10^{-19}\,\mathrm J)

. Use

c=3.00\times10^8\,\mathrm{m\,s^{-1}}

Maximum photoelectron kinetic energy in units of 10 to the minus 19 J versus reciprocal wavelength in units of 10 to the 6 inverse metres. A fitted line starts at threshold x=1.25 and passes through A at (2,1.5) and B at (4,5.5). No negative kinetic energies are plotted.

Use the gradient to estimate Planck's constant.

[3 marks]

Determine the threshold wavelength using this fitted model.

[2 marks]

Will increasing the intensity of

1000\,\mathrm{nm}

light cause ordinary single-photon photoemission from this metal? Explain.

[1 mark]

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WORKED SOLUTION

Practice marking scheme

6 marks

ANSWER

(a)

6.67\times10^{-34}\,\mathrm{J\,s}

. (b)

800\,\mathrm{nm}

. (c) No; its photons are below threshold.

Worked solution

(a)

E_{k,\max}=hc(1/\lambda)-W

, so the gradient is hc. The gradient is

(5.50-1.50)10^{-19}/[(4.00-2.00)10^6]=2.00\times10^{-25}\,\mathrm{J\,m}

. Thus

h=s/c=6.66667\times10^{-34}\,\mathrm{J\,s}

(b) Using A,

W=s(2.00\times10^6)-1.50\times10^{-19}=2.50\times10^{-19}\,\mathrm J

. At threshold

s/\lambda_0=W

, giving

\lambda_0=s/W=8.00\times10^{-7}\,\mathrm m=800\,\mathrm{nm}

(c)

1000\,\mathrm{nm}>800\,\mathrm{nm}

, so each photon has less energy than the work function. Higher intensity increases photon number, not photon energy; ordinary single-photon emission remains absent.

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: Calculate the SI gradient from the stated points.

[1 mark]

Part a: Identify this reciprocal-wavelength gradient as hc.

[1 mark]

Part a: Divide by c to estimate h.

[1 mark]

Part b: Obtain the work function from the fitted line.

[1 mark]

Part b: Calculate the threshold wavelength using the fit.

[1 mark]

Part c: Use the threshold and distinguish photon energy from photon number.

[1 mark]

Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.

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Quantum theory — Question 239

QUESTION 239 (6 marks)

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