The Universe

1. Overview

This topic explores the vast scale of our Universe, from our home galaxy, the Milky Way, to the billions of other galaxies moving away from us. By studying the light from these distant objects, scientists have uncovered evidence for the Big Bang Theory and can even estimate the age of the Universe itself.

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Key Definitions

• The Universe: A vast collection of billions of galaxies.
• Galaxy: A large system of billions of stars, gas, and dust bound together by gravity.
• Milky Way: The specific galaxy that contains our Solar System.
• Light-year: The distance light travels in one year (approximately $9.5 \times 10^{15}$ meters).
• Redshift: The increase in the observed wavelength of electromagnetic radiation from objects moving away from the observer.
• Cosmic Microwave Background Radiation (CMBR): (Extended) Weak microwave radiation coming from every direction in space, left over from the Big Bang.
• Hubble Constant ($H_0$): (Extended) The ratio of the speed at which a galaxy is moving away to its distance from Earth.

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Core Content

The Milky Way

• The Universe is made up of billions of galaxies.
• Our Solar System is a tiny part of the Milky Way galaxy.
• The diameter of the Milky Way is approximately 100,000 light-years.
• 📊A spiral-shaped galaxy with a label showing the Sun located on one of the outer spiral arms, far from the center.

Redshift

• When a star or galaxy moves away from Earth, the light waves it emits are "stretched."
• This stretching increases the wavelength, shifting the light toward the red end of the visible spectrum. This is called redshift.
• Light from distant galaxies is redshifted compared to light emitted on Earth.

The Expanding Universe

• Observations show that light from nearly all distant galaxies is redshifted.
• This proves that distant galaxies are receding (moving away) from us.
• The further away a galaxy is, the greater its redshift, meaning it is moving faster.
• This is key evidence that the Universe is expanding and supports the Big Bang Theory (the idea that the Universe began from a single, hot, dense point).

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Extended Content (Extended Only)

Cosmic Microwave Background Radiation (CMBR)

• CMBR is microwave radiation observed at all points in space around us.
• It was produced shortly after the Universe was formed as high-energy (short wavelength) radiation.
• As the Universe expanded, the space itself stretched. This stretched the radiation’s wavelength into the microwave region of the electromagnetic spectrum.
• CMBR is considered the "afterglow" of the Big Bang.

Measuring Space

• Speed ($v$): The speed at which a galaxy moves away can be calculated from the specific change in the wavelength of its starlight (the amount of redshift).
• Distance ($d$): The distance to very far galaxies is determined by observing the brightness of a supernova (an exploding star) within that galaxy.

The Hubble Constant and Age of the Universe

• The speed of recession ($v$) is proportional to the distance ($d$). This is Hubble’s Law.
• Equation: $v = H_0 d$
• The current estimate for $H_0$ is $2.2 \times 10^{-18}$ per second ($s^{-1}$).
• The age of the Universe can be estimated using the formula: $\text{Age} = \frac{1}{H_0}$.
• This calculation suggests the Universe started at a single point billions of years ago.

Worked Example 1: Galaxy speed from distance Calculate the speed of a galaxy that is $2.0 \times 10^{24}$ m away.

• $v = H_0 \times d$
• $v = (2.2 \times 10^{-18}) \times (2.0 \times 10^{24})$
• $v = 4.4 \times 10^6 \text{ m/s}$

Worked Example 2: Estimating the age of the Universe Using $H_0 = 2.2 \times 10^{-18}\text{ s}^{-1}$:

• Age $= 1 / H_0 = 1 / (2.2 \times 10^{-18}) = 4.5 \times 10^{17}\text{ s}$
• To convert to years: $4.5 \times 10^{17} / (365 \times 24 \times 3600) \approx 1.4 \times 10^{10}\text{ years}$ (about 14 billion years)

You must memorise the value of $H_0 = 2.2 \times 10^{-18}\text{ per second}$ — it appears in every exam question on this topic.

Worked Example 3: Converting light-years to metres Show that 1 light-year $\approx 9.5 \times 10^{15}\text{ m}$.

• 1 year = $365 \times 24 \times 3600 = 3.15 \times 10^{7}\text{ s}$
• 1 light-year = $c \times t = 3.0 \times 10^{8} \times 3.15 \times 10^{7} = 9.5 \times 10^{15}\text{ m}$

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Key Equations

Equation	Symbols	Units
$v = H_0 d$	$v$: speed, $d$: distance, $H_0$: Hubble constant	$v$ (m/s), $d$ (m), $H_0$ ($s^{-1}$)
$t = \frac{1}{H_0}$	$t$: Age of the Universe	$t$ (seconds)

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Common Mistakes to Avoid

• ❌ Wrong: Thinking the Sun is at the center of the Universe.
• ✅ Right: The Sun is just one star in the Milky Way, and it is not at the center of the galaxy or the Universe.
• ❌ Wrong: Defining redshift as a change in the speed of light.
• ✅ Right: Redshift is a change in wavelength. The speed of light ($c$) is constant.
• ❌ Wrong: Confusing a galaxy with a Solar System.
• ✅ Right: A Solar System is one star and its planets; a galaxy contains billions of stars and solar systems.
• ❌ Wrong: Thinking redshift means the light looks red to the naked eye.
• ✅ Right: It means the wavelength is longer than expected, not necessarily that the object appears red.

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Exam Tips

1. Definitions Matter: If asked to describe redshift, always mention the "increase in observed wavelength" and that the source is "moving away/receding."
2. Unit Conversions: In Hubble Constant calculations, ensure distance is in meters (m) and speed is in meters per second (m/s).
3. Big Bang Evidence: If a question asks for evidence of the Big Bang, you must mention Redshift (Core) and CMBR (Extended).

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Exam-Style Questions

Practice these original exam-style questions to test your understanding. Each question mirrors the style, structure, and mark allocation of real Cambridge 0625 Theory papers.

Exam-Style Question 1 — Short Answer [5 marks]

Question:

(a) State the name of the galaxy that contains our solar system. [1]

(b) The diameter of this galaxy is approximately 100,000 light-years. Define what is meant by the term 'light-year'. [2]

(c) Explain how the observation of redshift in the light from distant galaxies provides evidence for the Big Bang Theory. [2]

Worked Solution:

(a)

1. The name of our galaxy is the Milky Way. $\boxed{\text{Milky Way}}$ [Recall of factual information]

How to earn full marks:

• Correct spelling is not required but the answer must be unambiguous.

(b)

1. A light-year is a measure of distance. [Conceptual understanding]

2. Specifically, it's the distance that light travels in one year. [Precise definition]

How to earn full marks:

• For 2 marks: "The distance light travels in one year".
• For 1 mark: "The distance light travels in a long time", OR "a very long distance".

(c)

1. Redshift indicates that the wavelength of light from distant galaxies is increased, meaning they are moving away from us. [Linking redshift to receding galaxies]

2. If all galaxies are moving away from us, it suggests that the Universe is expanding from a single point, which is the fundamental idea of the Big Bang Theory. [Connecting expansion to the Big Bang]

How to earn full marks:

• Mention redshift and receding galaxies for one mark.
• Link the receding galaxies to the expansion of the universe and the Big Bang for the second mark.

Common Pitfall: Many students confuse a light-year as a unit of time. Remember it's a unit of distance. Also, be clear that redshift implies galaxies are moving away from us, not just moving in general.

Exam-Style Question 2 — Short Answer [6 marks]

Question:

(a) State what is meant by the term cosmic microwave background radiation (CMBR). [2]

(b) Explain how the CMBR supports the Big Bang Theory. [2]

(c) State two pieces of evidence, other than CMBR, that support the Big Bang Theory. [2]

Worked Solution:

(a)

1. CMBR is a form of electromagnetic radiation. [Identifying CMBR as radiation]

2. It is microwave radiation of a specific frequency that is observed at all points in space. [Describing the radiation's properties and distribution]

How to earn full marks:

• "Microwave radiation" or "electromagnetic radiation" for one mark.
• "Observed everywhere" or "fills the universe" for the second mark.

(b)

1. The Big Bang Theory predicts that the early Universe was extremely hot and dense. [Stating the initial conditions]

2. As the Universe expanded, this radiation cooled and stretched, eventually becoming the CMBR we observe today. [Connecting the early Universe to the observed radiation]

How to earn full marks:

• Mention the early universe was hot and dense for one mark.
• Link the cooling and expansion of this radiation to the CMBR for the second mark.

(c)

1. The abundance of light elements (hydrogen and helium). [Factual recall]

2. The redshift of distant galaxies. [Factual recall]

How to earn full marks:

• Any two of:
  • Abundance of light elements (H and He)
  • Redshift of distant galaxies
  • Large scale structure of the universe (galaxy distribution)

Common Pitfall: Don't just say "radiation" for CMBR. You need to specify that it's microwave radiation. Also, remember that the CMBR is a consequence of the Big Bang's prediction of a hot, dense early universe that has since cooled.

Exam-Style Question 3 — Extended Response [7 marks]

Question:

A distant galaxy is observed to have a redshift, indicating that it is moving away from Earth at a speed of $6.6 \times 10^6 , \text{m/s}$.

(a) Calculate the approximate distance of the galaxy from Earth, using a Hubble constant ($H_0$) of $2.2 \times 10^{-18} , \text{s}^{-1}$. [3]

(b) A supernova is observed in this galaxy. Describe how the brightness of the supernova can be used to independently determine the distance to the galaxy. [2]

(c) Explain why determining the distances to galaxies is important for understanding the evolution of the Universe. [2]

Worked Solution:

(a)

1. Recall the Hubble's Law equation. $v = H_0 d$ [Stating the relevant equation]

2. Rearrange the equation to solve for distance. $d = \frac{v}{H_0}$ [Rearranging the equation]

3. Substitute the values and calculate the distance. $d = \frac{6.6 \times 10^6 , \text{m/s}}{2.2 \times 10^{-18} , \text{s}^{-1}} = 3.0 \times 10^{24} , \text{m}$ $\boxed{d = 3.0 \times 10^{24} , \text{m}}$ [Substituting values and calculating the answer]

How to earn full marks:

• Correct equation for 1 mark.
• Correct rearrangement for 1 mark.
• Correct answer (with unit) for 1 mark.

(b)

1. Supernovae have a known intrinsic brightness (absolute magnitude). [Stating a key property of supernovae]

2. By comparing the observed brightness (apparent magnitude) with the known intrinsic brightness, the distance can be determined using the inverse square law. [Explaining the method based on brightness comparison]

How to earn full marks:

• Mention that supernovae have a known brightness for one mark.
• Explain the comparison between observed and intrinsic brightness to determine distance for the second mark.

(c)

1. Distances to galaxies allow us to map the structure of the Universe, including the distribution of galaxies and the existence of large-scale structures. [Relating distance to the Universe's structure]

2. By understanding the distances and speeds of galaxies, we can study the expansion rate of the Universe over time, which provides insights into its past and future evolution. [Relating distance to understanding the expansion and evolution of the Universe]

How to earn full marks:

• Mention mapping the structure of the universe for one mark.
• Link distances to the expansion rate and evolution of the universe for the second mark.

Common Pitfall: Remember to include the unit (metres) in your final answer for part (a). Also, for supernovae, it's crucial to understand that we compare the observed brightness to the known intrinsic brightness to estimate distance.

Exam-Style Question 4 — Extended Response [9 marks]

Question:

A scientist measures the wavelength of a specific spectral line in the light emitted from a distant galaxy. The measured wavelength is 660 nm. The same spectral line, when measured in a laboratory on Earth, has a wavelength of 600 nm.

(a) Show that the galaxy is receding from Earth at a speed of $3.0 \times 10^7 , \text{m/s}$. The speed of light is $3.0 \times 10^8 , \text{m/s}$. [3]

(b) Calculate the distance to the galaxy in metres, using a Hubble constant ($H_0$) of $2.2 \times 10^{-18} , \text{s}^{-1}$. [2]

(c) Calculate an estimate for the age of the Universe in years, using the Hubble constant given in part (b). Assume 1 year = $3.2 \times 10^7$ seconds. [3]

(d) Explain why the age calculated in part (c) is only an estimate. [1]

Worked Solution:

(a)

1. State the formula for redshift. $z = \frac{\Delta \lambda}{\lambda_0} = \frac{\lambda_{observed} - \lambda_{rest}}{\lambda_{rest}}$ [Stating the redshift formula]

2. Calculate the redshift. $z = \frac{660 \text{ nm} - 600 \text{ nm}}{600 \text{ nm}} = 0.1$ [Calculating the redshift value]

3. Use the redshift to calculate the velocity. $v = z \times c = 0.1 \times 3.0 \times 10^8 , \text{m/s} = 3.0 \times 10^7 , \text{m/s}$ $\boxed{v = 3.0 \times 10^7 , \text{m/s}}$ [Calculating the receding velocity]

How to earn full marks:

• Correct redshift equation for 1 mark.
• Correct calculation of redshift z for 1 mark.
• Correct calculation of velocity with correct units for 1 mark.

(b)

1. Recall Hubble's Law. $v = H_0 d$ [Stating Hubble's Law]

2. Rearrange and calculate the distance. $d = \frac{v}{H_0} = \frac{3.0 \times 10^7 , \text{m/s}}{2.2 \times 10^{-18} , \text{s}^{-1}} = 1.36 \times 10^{25} , \text{m}$ $\boxed{d = 1.36 \times 10^{25} , \text{m}}$ [Calculating the distance]

How to earn full marks:

• Correct rearrangement of Hubble's law for 1 mark.
• Correct distance with correct units for 1 mark. ECF from (a) is allowed.

(c)

1. State the formula for the age of the Universe. $t = \frac{1}{H_0}$ [Stating the age formula]

2. Calculate the age in seconds. $t = \frac{1}{2.2 \times 10^{-18} , \text{s}^{-1}} = 4.55 \times 10^{17} , \text{s}$ [Calculating the age in seconds]

3. Convert to years. $t = \frac{4.55 \times 10^{17} , \text{s}}{3.2 \times 10^7 , \text{s/year}} = 1.42 \times 10^{10} , \text{years}$ $\boxed{t = 1.42 \times 10^{10} , \text{years}}$ [Converting to years]

How to earn full marks:

• Correct equation for age of the universe for 1 mark.
• Correct age in seconds for 1 mark.
• Correct age in years for 1 mark. ECF from (b) is allowed.

(d)

1. The Hubble constant is not truly constant and its value has changed over time. [Explaining the limitation of the Hubble constant]

How to earn full marks:

• The Hubble constant is not constant (it changes with time).

Common Pitfall: Be careful with unit conversions, especially when converting seconds to years. Also, remember that the Hubble constant is not truly constant, which makes the age calculation only an estimate.