Stars and the Universe Worked ExamplesIGCSE Physics 0625

The Sun is a medium-sized star consisting mostly of hydrogen and helium. So the answer is C.

A is wrong on both size and composition. B is wrong because the Sun radiates most of its energy in the infrared, visible and ultraviolet regions. D is wrong twice: stable stars are powered by nuclear fusion (joining nuclei), and it is hydrogen that is fused into helium, not the other way round.

(a) A light-year is the distance travelled by light in (the vacuum of) space in one year.

(b) Divide the distance in metres by the number of metres in one light-year.

(c) Multiply the number of light-years by the metres in one light-year.

When most of the hydrogen in the centre has been converted to helium, a star expands. A less massive star forms a red giant (1). A more massive star forms a red supergiant (4).

A red giant from a less massive star forms a planetary nebula (2), with a white dwarf (3) at its centre.

A red supergiant explodes as a supernova. It forms a nebula containing hydrogen and new heavier elements (5), and leaves behind a neutron star or a black hole (6) at its centre.

(a) Force X (inwards) is caused by the star's own gravitational attraction. Force Y (outwards) is due to the high temperature in the centre of the star.

(b) A protostar is an interstellar cloud that is collapsing under its internal gravitational attraction, and its temperature increases as it does. It becomes a stable star when the inward force of gravitational attraction is balanced by the outward force due to the high temperature at its centre.

(c) All stars eventually run out of hydrogen as fuel for the nuclear fusion reactions, so the balance cannot last. The star then expands.

(a) Redshift is an increase in the observed wavelength of electromagnetic radiation (light) emitted from a star or galaxy that is moving away from us, compared with the wavelength emitted by the same source at rest (as measured on Earth).

(b) Galaxy B. Its lines are shifted further towards longer wavelengths, so it has a greater redshift. The change in wavelength is used to find the speed at which a galaxy moves away, and a larger shift means a larger speed.

(c) The redshift of light from distant galaxies is evidence that the Universe is expanding, and it supports the Big Bang Theory.

The CMBR was produced shortly after the Universe was formed. As the Universe expanded, this radiation was stretched into the microwave region, so its wavelength has increased. That is B.

C has the direction of the change backwards: the wavelength was shorter in the past. A is wrong because microwave radiation of a specific frequency is observed at all points in space around us, not from one direction. D confuses the CMBR with background radiation from rocks, which is ionising nuclear radiation.

$H_0 = v/d$, which is the gradient of the best-fit line. Choose a point far along the line (not a data cross), e.g. at $d = 4.0 \times 10^{24}$ m the line gives $v = 9200$ km/s.

Convert the speed to m/s: $9200$ km/s $= 9.2 \times 10^{6}$ m/s.

(b) Any sensible reason: the distances (and speeds) of the galaxies have uncertainties; the sample is only six galaxies; the line is drawn by eye.

(a) Write the equation and rearrange it for $d$.

Convert the speed: $4400$ km/s $= 4.4 \times 10^{6}$ m/s. Substitute.

(b) Divide by the number of metres in one light-year.

(a) The distance of the galaxy from the Earth.

(b) The change in wavelength of the starlight due to redshift (compared with the wavelength emitted on Earth).

(c) Convert the distance to metres.

Write the equation and substitute.

$2.17 \times 10^{-18}$ s⁻¹ rounds to $2.2 \times 10^{-18}$ s⁻¹, as required.

A massive star earlier in the history of the galaxy expanded into a red supergiant and then exploded as a supernova.

The supernova formed a nebula containing hydrogen and new heavier elements.

Material from such a nebula can form new stars with orbiting planets. The Sun and its planets formed from this material, so the planets contain the heavier elements.

(a) Divide distance by speed for each galaxy.

The line on the graph passes through the origin, so $d/v$ (its gradient) is the same for every galaxy. It is also $1/H_0$: with $H_0 = 2.2 \times 10^{-18}$ s⁻¹, $1/H_0 = 4.5 \times 10^{17}$ s.

(b) If every galaxy has moved at a constant speed, $d/v$ is the time since each galaxy was at the same place as us. It is the same for all galaxies, so it is an estimate of the age of the Universe, and it is evidence that all the matter in the Universe was present at a single point.

(c) Divide by the number of seconds in a year.

(a) Convert each speed to m/s and divide by the distance in metres. For G1:

The same for the others (all $\times 10^{-18}$ s⁻¹):

(b) G3 ($1.14 \times 10^{-18}$ s⁻¹) is about half the others, so it is anomalous. Leave it out of the mean.

(c) The mean, $2.2 \times 10^{-18}$ s⁻¹ to 2 significant figures, agrees with the current estimate.

(d) The distance of G3 may have been overestimated (for example, if the brightness of its supernova was misjudged, since supernova brightness is used to find distance), or its speed was measured wrongly from its redshift.