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.

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.

 In the laboratory, the same spectral line has wavelength 656 nm.

(i) Calculate the speed of the galaxy.

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.

(c) In the laboratory, the same spectral line has wavelength 656 nm.

(ii) State the direction of travel of the galaxy.

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.

State and explain what the wavelength of the same spectral line would be for a much more distant galaxy.

Neptune is the farthest known planet from the Sun in the Solar System. Its distance from the Sun is 30 times greater than the distance of the Earth from the Sun. The radiant flux intensity from the Sun at the Earth is $1400 \mathrm{W} {\mathrm{m}}^{-2}$.

A space probe is close to Neptune.

Calculate the maximum radiant power received by an instrument of cross-sectional area $1.0 {\mathrm{cm}}^2$ on this space probe.