Quantum theory — Question 183

Original QCE Vault practice · 6 marks

Q183 · Practice questionComplex unfamiliar6 marks

QUESTION 183 (6 marks)

The graph shows maximum photoelectron kinetic energy for metals M and N. Line M passes through

(6.00\times10^{14}\,\mathrm{Hz},1.3252\times10^{-19}\,\mathrm J)

and

(9.00\times10^{14}\,\mathrm{Hz},3.3130\times10^{-19}\,\mathrm J)

. The frequency intercept of N is

6.00\times10^{14}\,\mathrm{Hz}

. Assume straight-line fits.

Maximum kinetic energy in 10 to the minus 19 J versus frequency in 10 to the 14 Hz. Parallel lines M and N start at thresholds 4 and 6, respectively. No negative kinetic energies are plotted.

Determine an experimental value of Planck's constant from line M.

[2 marks]

Determine the work function of M.

[2 marks]

Determine the work function of N and explain why it is greater than that of M.

[2 marks]

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WORKED SOLUTION

Practice marking scheme

6 marks

ANSWER

(a)

h=6.626\times10^{-34}\,\mathrm{J\,s}

. (b)

W_M=2.6504\times10^{-19}\,\mathrm J

. (c)

W_N=3.9756\times10^{-19}\,\mathrm J

; N requires a higher photon energy for emission.

Worked solution

(a)

E_{k,\max}=hf-W

gives gradient

h

. Therefore

h=(3.3130-1.3252)10^{-19}/[(9.00-6.00)10^{14}]=6.626\times10^{-34}\,\mathrm{J\,s}

(b)

W_M=hf-E_k=(6.626\times10^{-34})(6.00\times10^{14})-1.3252\times10^{-19}=2.6504\times10^{-19}\,\mathrm J

. Its threshold is

W_M/h=4.00\times10^{14}\,\mathrm{Hz}

(c)

W_N=hf_{0,N}=(6.626\times10^{-34})(6.00\times10^{14})=3.9756\times10^{-19}\,\mathrm J

. Its greater threshold frequency means a larger minimum photon energy is needed to remove an electron. The equal slopes describe the universal h, not equal work functions.

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 the gradient as Planck constant.

[1 mark]

Part a: Calculate it with both axis scale factors.

[1 mark]

Part b: Use a point and the gradient to calculate the work function.

[1 mark]

Part b: Obtain the correct positive work function.

[1 mark]

Part c: Calculate the second work function from its threshold.

[1 mark]

Part c: Explain the threshold difference in photon-energy terms.

[1 mark]

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

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Quantum theory — Question 183

QUESTION 183 (6 marks)

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