Edexcel iGCSE Physics (4PH1) 8.2 Motion in the Universe Exam Style Question Paper 2B - New Syllabus
Question
This question is about cosmic microwave background radiation (CMBR) and the Big Bang.
(a) CMBR has a mean frequency of \(1.6\times10^{11}\,\mathrm{Hz}\).
(i) State the formula linking wave speed, frequency and wavelength. (1)
(ii) Show that the mean wavelength of CMBR is about \(2\,\mathrm{mm}\). (3)
[speed of light \(=3.0\times10^8\,\mathrm{m\,s^{-1}}\)]
(b) CMBR was first released after the Big Bang.
When CMBR was first released it had a wavelength of about \(9\times10^{-5}\,\mathrm{mm}\), but now it has a wavelength of about \(2\,\mathrm{mm}\).
Using this information, explain how CMBR supports the Big Bang theory. (2)
(c) Explain how the cosmological red-shift of galaxies also supports the Big Bang theory. (4)
Syllabus Topic Codes (Edexcel International GCSE Physics 4PH1):
• 8.13–8.14P: The Big Bang Theory and its evidence — part (b)
• 8.15–8.16P: Red-shift, motion of galaxies and the red-shift equation — part (c)
• 8.17P: Red-shift and distance — relevant to part (c)
• 8.18P: Expansion of the Universe — relevant to parts (b) and (c)
▶️ Answer/Explanation
(a)(i) Wave speed equation [1 mark]
The relationship between wave speed, frequency and wavelength is
\(v=f\lambda\)
Final Answer: \( \boxed{v=f\lambda} \)
(a)(ii) Mean wavelength of CMBR [3 marks]
1. Use the wave equation:
\(v=f\lambda\)
2. Rearrange for wavelength:
\(\lambda=\dfrac{v}{f}\)
3. Substitute the values:
\(\lambda=\dfrac{3.0\times10^8}{1.6\times10^{11}}\)
\(\lambda=1.875\times10^{-3}\,\mathrm{m}\)
Since \(1\,\mathrm{m}=1000\,\mathrm{mm}\):
\(\lambda=1.875\,\mathrm{mm}\approx1.9\,\mathrm{mm}\)
Final Answer: \( \boxed{1.9\,\mathrm{mm}\approx2\,\mathrm{mm}} \)
(b) CMBR as evidence for the Big Bang [2 marks]
- The wavelength of CMBR has increased over time, from about \(9\times10^{-5}\,\mathrm{mm}\) to about \(2\,\mathrm{mm}\).
- This is evidence that the Universe is expanding, which supports the Big Bang theory.
Final Answer: The wavelength of CMBR has increased since it was first released, showing that the Universe has expanded. This supports the Big Bang theory because the theory predicts an expanding Universe.
(c) Cosmological red-shift and the Big Bang [4 marks]
- Most galaxies show a red-shift, indicating that they are moving away from the Earth and from each other.
- More distant galaxies show a greater red-shift.
- This indicates that more distant galaxies are travelling away from us faster.
- This provides evidence that the Universe is expanding, so the matter in the Universe must have originated from a much smaller, concentrated state, supporting the Big Bang theory.
Final Answer: Most galaxies are red-shifted, showing that they are moving away from Earth. More distant galaxies have a greater red-shift and are therefore moving away faster. This shows that the Universe is expanding, supporting the idea that all matter originated from a single point or very small region in the Big Bang.
Question
A binary star system has two nearby stars, which orbit each other in a circular path around a common centre of gravity.
(a) In an eclipsing binary system, one star passes behind the other star in its orbit. This causes a decrease in the light intensity of the binary star system when viewed from Earth. The graph shows how the light intensity of the binary star system changes with time.
(i) Suggest why the decreases in light intensity are not all the same.
(ii) Use the graph to determine the time period of the binary star system.
(iii) One of the stars in this binary system has an orbital speed of \(19\,\mathrm{km\,s^{-1}}\). Calculate the orbital radius of this star.
(b) A different binary star system is in a distant galaxy. When observed from the Earth, light from this galaxy has a longer wavelength than the wavelength of the light when it is emitted from the galaxy. Explain why this gives evidence for the Big Bang theory.
Syllabus Topic Codes (Edexcel International GCSE Physics 4PH1):
• 8.6: Orbital Speed, Radius, and Time Period — parts (a)(ii)–(iii)
• 8.13–8.14P: The Big Bang Theory and Its Evidence — part (b)
• 8.15–8.16P: Red-Shift, Motion of Galaxies, the Red-Shift Equation — part (b)
▶️ Answer/Explanation
(a)(i) Different decreases in light intensity [1 mark]
The two stars are not necessarily the same size, brightness, mass, temperature or luminosity.
Therefore, the decrease in light intensity depends on which star is passing in front of the other.
(a)(ii) Time period [1 mark]
The time period is the time between two identical points in successive cycles, such as two successive large decreases in light intensity.
From the graph:
\(\boxed{T\approx31\,\mathrm{years}}\)
(a)(iii) Orbital radius [4 marks]
For circular motion, the distance travelled in one complete orbit is:
\(\displaystyle d=2\pi r\)
Since \(\displaystyle v=\frac{d}{t}\):
\(\displaystyle v=\frac{2\pi r}{T}\)
Rearranging:
\(\displaystyle r=\frac{vT}{2\pi}\)
Convert \(31\) years into seconds:
\(\displaystyle T=31\times365\times24\times3600\)
\(\displaystyle T\approx9.78\times10^8\,\mathrm{s}\)
Substitute \(v=19\,\mathrm{km\,s^{-1}}\):
\(\displaystyle r=\frac{19\times9.78\times10^8}{2\pi}\)
\(\displaystyle r\approx2.96\times10^9\,\mathrm{km}\)
Therefore:
\(\boxed{r\approx3.0\times10^9\,\mathrm{km}}\)
(b) Evidence for the Big Bang [4 marks]
- The light from the distant galaxy has been red-shifted, because its observed wavelength is longer than its emitted wavelength.
- Red-shift provides evidence that the galaxy is moving away from Earth.
- This shows that galaxies are moving apart, providing evidence that the Universe is expanding.
- If the Universe is expanding, tracing the expansion backwards suggests that the Universe was once concentrated at a single point, supporting the Big Bang theory.
Thus, the observed red-shift of distant galaxies provides evidence for an expanding Universe and therefore supports the Big Bang theory.