2024HSCShort answer

Q24 (b)

3 marks

Question

An absorption spectrum resulting from the passage of visible light from a star’s surface through its hydrogen atmosphere is shown. Absorption lines are labelled W to Z in the diagram.

Absorption line $W$ originates from an electron transition between the second and sixth energy levels. Use

\frac{1}{\lambda} = R\left(\frac{1}{n_f^2} - \frac{1}{n_i^2}\right)

to calculate the frequency of light absorbed to produce absorption line $W$ .

Uncropped source page 22 for question 24.b; requires human review and cropping — Reviewed visual · source page 22

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Solution

Criteria	Marks
Calculates the frequency of light associated with absorption line $W$ using provided equation	3
Provides a correct calculation	2
Provides a relevant step	1

Sample answer: Using the relationship, and treating it as an emission spectrum:

\frac{1}{\lambda} = 1.097 \times 10^7\left(\frac{1}{2^2} - \frac{1}{6^2}\right) = 2.44 \times 10^6\ \mathrm{m}^{-1}

Wavelength is therefore $4.1 \times 10^{-7}\ \mathrm{m}$ . So $f = \frac{c}{\lambda} = 7.3 \times 10^{14}\ \mathrm{Hz}$ .

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Syllabus alignment

Module 8 · From the Universe to the Atom

Quantum Mechanical Nature of the AtomEvaluate Rutherford and Bohr models and use hydrogen line spectra and quantised energy levels.

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