QCE Physics: Quantum theory Q185

Quantum theory — Question 185

Original QCE Vault practice · 7 marks

Q185 · Practice questionComplex unfamiliar7 marks

QUESTION 185 (7 marks)

An idealised atom has bound energy levels

-8.00

-3.00

and

-1.00\,\mathrm{eV}

, with ionisation at

0\,\mathrm{eV}

. Its electron initially occupies the ground level. Incident photons have energies

4.00

5.00

7.00

8.50\,\mathrm{eV}

. Ignore recoil and multi-photon processes. Use

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

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

and

1\,\mathrm{eV}=1.60\times10^{-19}\,\mathrm J

Energy-level diagram: ground state -8.00 eV, excited levels -3.00 and -1.00 eV, and a dashed ionisation level at zero. Energies and states occupy separate columns. Schematic spacing, not to scale.

Identify which photons can cause bound-state absorption, which can ionise, and which cannot be absorbed under this model.

[3 marks]

Determine the kinetic energy of an electron ejected by an

8.50\,\mathrm{eV}

photon, in joules.

[2 marks]

Determine the wavelength of a photon emitted in a transition from

-1.00

-3.00\,\mathrm{eV}

[2 marks]

Question linkSyllabus coverage

WORKED SOLUTION

Practice marking scheme

7 marks

ANSWER

(a)

5.00

and

7.00\,\mathrm{eV}

cause bound-state absorption;

8.50\,\mathrm{eV}

can ionise;

4.00\,\mathrm{eV}

cannot be absorbed. (b)

8.00\times10^{-20}\,\mathrm J

. (c)

621\,\mathrm{nm}

Worked solution

(a) Ground-to-bound gaps are

-3-(-8)=5.00

and

-1-(-8)=7.00\,\mathrm{eV}

. Ionisation needs at least

8.00\,\mathrm{eV}

, so

8.50\,\mathrm{eV}

can eject the electron. No bound gap matches

4.00\,\mathrm{eV}

, and it is below ionisation threshold.

(b) Energy conservation gives

E_k=8.50-8.00=.500\,\mathrm{eV}

. Converting,

E_k=.500(1.60\times10^{-19})=8.00\times10^{-20}\,\mathrm J

2.00\,\mathrm{eV}=3.20\times10^{-19}\,\mathrm J

. Thus

\lambda=hc/E=6.211875\times10^{-7}\,\mathrm m=621.188\,\mathrm{nm}

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 both matching bound-state photon energies.

[1 mark]

Part a: Identify the above-threshold ionising photon.

[1 mark]

Part a: Reject the nonmatching sub-threshold photon.

[1 mark]

Part b: Subtract the ionisation energy from photon energy.

[1 mark]

Part b: Convert the residual energy to joules.

[1 mark]

Part c: Use the magnitude of the specified energy gap.

[1 mark]

Part c: Convert units and calculate wavelength.

[1 mark]

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

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Quantum theory — Question 185

QUESTION 185 (7 marks)

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