The recession speed $v$ against distance $d$ graph for some galaxies is shown.

Determine the Hubble constant from this graph. Explain your answer.

The Big Bang occurred some 14 billion years ago.

$1 \text{years} \approx 3.15\times {10}^{-7}\mathrm{s}$

Estimate the farthest distance we can observe. Explain your answer.

The surface temperature $T$ of a star depends on the wavelength ${\lambda }_{\max }$ at the peak intensity of the emitted radiation from the star. The $T$ against ${\lambda }_{\max }$ graph for a cluster of stars in our galaxy is shown.

Use the graph to show Wien's displacement law is obeyed.

The surface temperature $T$ of a star depends on the wavelength ${\lambda }_{\max }$ at the peak intensity of the emitted radiation from the star. The $T$ against ${\lambda }_{\max }$ graph for a cluster of stars in our galaxy is shown.

(ii) Estimate the surface temperature of a star with ${\lambda }_{max}=400\pm 10 \mathrm{nm}$. In your answer, include the absolute uncertainty.

Light from a galaxy is passed through a diffraction grating. The diagram shows part of the emission spectrum.

The strong emission spectral line has wavelength $662 \mathrm{nm}$.

Calculate the energy of a photon of wavelength $662 \mathrm{nm}$.

Light from a galaxy is passed through a diffraction grating. The diagram shows part of the emission spectrum.

The strong emission spectral line has wavelength 662 nm.

Explain how a spectral line is produced by electrons within atoms.