Physics 9702 · AS & A Level · Energy levels in atoms and line spectra

Energy levels in atoms and line spectra — practice question

Fig. 8.1 shows a section of the visible emission spectrum produced by hydrogen gas in a star within a galaxy that is far away. That galaxy is receding from Earth at a speed of $6.2 \times 10^{6}\,\text{m s}^{-1}$.
(a(i))[2]

Explain how the line positions in the emission spectrum recorded by an observer on Earth are different from those shown in Fig. 8.1.

(a(ii))[2]

On Fig. 8.1, draw the three lines in positions that could be seen in the spectrum observed by the observer.

(b(i))[2]

The lines in Fig. 8.1 are due to electron transitions to the energy level $-3.40\,\text{eV}$. One of the lines shows emitted radiation with wavelength $488\,\text{nm}$. Calculate the energy of a photon of this radiation.

(b(ii))[2]

Determine the energy, in $\text{eV}$, of the energy level from which the electron transition starts and which produces the emission of this radiation.

(b(iii))[2]

Determine the wavelength, in $\text{nm}$, of this radiation as observed on Earth.

(c)[2]

A value for the Hubble constant is $2.3 \times 10^{-18}\,\text{s}^{-1}$. Determine the distance of the galaxy from the Earth.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: The star’s motion leads to a change in observed frequency or redshift

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