Origin and Age of the Earth: Big Bang, Nebular and Planetesimal Hypotheses, Radioactive Dating, ISC Class 11

What Origin and Age of the Earth is about

Weightage: CISCE gives no Class XI unit weightage for ISC Geography. Origin and Age of the Earth is topic 1 of the Class XI syllabus (Formation of the Earth) and can be asked anywhere in the 70-mark Paper I (Theory, 3 hours). Class XI is examined by the school, so your school sets the paper and decides how many marks each topic carries.Source: CISCE ISC Geography (853) syllabus, examination year 2028, Class XI

Key concepts

The Big Bang theory

The Big Bang theory, also called the expanding universe hypothesis, is the most widely accepted explanation of the origin of the universe.

Stages
1. In the beginning all matter existed in one extremely small point (a 'singularity') of unimaginably high temperature and density.
2. About 13.7 billion years ago this point began to expand violently: the 'Big Bang'. There was very rapid expansion in the first fractions of a second, and some energy turned into matter.
3. Within the first few minutes the first atomic nuclei formed; after about 300,000 years the temperature fell to about 4,500 K, atoms formed and the universe became transparent.
4. Uneven distribution of matter caused gravity to draw it into clumps that became galaxies; within galaxies, clouds of gas (nebulae) condensed into stars.
5. Our solar system formed from such a nebula about 4.6 billion years ago.

Evidence

• Edwin Hubble showed (1920s) that galaxies are moving away from one another: the universe is expanding.
• Faint background radiation left from the early hot universe (cosmic microwave background) has been detected.
• The abundance of light elements (hydrogen and helium) matches the theory.

An alternative, Fred Hoyle's steady state theory, held that the universe was always roughly the same; the evidence for expansion led scientists to favour the Big Bang.

Worked example

[4] Explain the stages of the Big Bang theory and one piece of evidence for it. (Understanding)

Try it first, then show the solutionSolution

1. All matter in a single point of infinite density and temperature - 1 mark.
2. Expansion began about 13.7 billion years ago; energy turned into matter - 1 mark.
3. Atoms formed; galaxies and stars formed from clumps of matter - 1 mark.
4. Evidence: Hubble showed galaxies moving apart (expanding universe) - 1 mark.

Answer: All matter was once packed into a single point of infinite density and temperature, which began to expand violently about 13.7 billion years ago, turning energy into matter. As it cooled, atoms formed, and uneven gravity gathered matter into galaxies, whose gas clouds formed stars. Hubble's discovery that galaxies are moving apart shows that the universe is still expanding, supporting the theory.

The nebular hypothesis

Proposed by the German philosopher Immanuel Kant (1755) and developed by the French mathematician Pierre-Simon Laplace (1796).

Main ideas
1. The solar system began as a huge, hot, slowly rotating cloud of gas (the nebula).
2. As the cloud cooled, it contracted and rotated faster.
3. Laplace's version: the faster rotation flattened it and caused rings of material to separate from its outer edge; each ring condensed to form a planet, while the centre became the sun.
4. The planets therefore revolve in the same direction and roughly in one plane.

Strengths: it explains why planets move in the same direction around the sun and lie roughly in one plane.

Weaknesses: it cannot explain why the sun, which holds most of the mass, rotates so slowly while the planets hold most of the angular momentum; it is doubtful that rings of gas would condense into planets.

Revision: in about 1950 Otto Schmidt (Russia) and Carl Weizsacker (Germany) revised the idea: the sun was surrounded by a solar nebula of hydrogen, helium and dust; friction and collisions formed a disc, and planets grew by accretion. This forms the basis of modern views.

Worked example

[4] State the main features of the nebular hypothesis and one weakness. (Recall)

Try it first, then show the solutionSolution

1. Kant (1755), Laplace (1796); a hot, rotating nebula - 1 mark.
2. Cooling and contraction increased rotation - 1 mark.
3. Rings separated and condensed into planets; centre became the sun - 1 mark.
4. Weakness: the sun's slow rotation (angular momentum problem) - 1 mark.

Answer: Kant proposed and Laplace (1796) developed the idea that the solar system began as a hot, slowly rotating nebula, which cooled, contracted and spun faster, throwing off rings of material that condensed into planets while the centre became the sun. Its weakness is that it cannot explain why the sun, with most of the mass, spins so slowly while the planets carry most of the angular momentum.

The planetesimal hypothesis

Proposed by the American geologist T. C. Chamberlin and the astronomer F. R. Moulton in the early twentieth century.

Main ideas
1. The sun already existed when a passing star came close to it.
2. The star's gravity pulled out streams of gaseous matter from the sun.
3. This material cooled and solidified into a great many small solid bodies, called planetesimals.
4. The planetesimals moved in orbits around the sun; by repeated collision and gravitational attraction they stuck together (accretion) to form larger bodies, the planets and their moons.

Strengths: it explains the formation of planets by accretion of small solid bodies, an idea kept in modern theory.

Weaknesses: the chance of a star passing so close to the sun is extremely small, and hot gas pulled from the sun would probably disperse rather than condense.

Modern view: planets formed by the accretion of planetesimals within the disc of gas and dust (solar nebula) around the young sun, combining the nebular and planetesimal ideas:
(i) a rotating disc of gas and dust formed around a gas core; (ii) matter condensed into small rounded planetesimals; (iii) planetesimals collided and accreted into a few large planets.

Worked example

[4] Explain the planetesimal hypothesis of the origin of the earth. (Understanding)

Try it first, then show the solutionSolution

1. Chamberlin and Moulton: a passing star approached the sun - 1 mark.
2. Its gravity drew out matter from the sun - 1 mark.
3. The matter cooled into small solid planetesimals - 1 mark.
4. Planetesimals collided and accreted into planets - 1 mark.

Answer: Chamberlin and Moulton suggested that a star passing close to the sun drew streams of matter out of it by its gravity. This matter cooled and solidified into countless small solid bodies, planetesimals, which orbited the sun and, through repeated collisions and gravitational attraction, accreted into the planets.

Radioactive dating: principle

Principle
1. Some elements are radioactive: their atoms (parent isotopes) break down spontaneously into other atoms (daughter isotopes), giving off radiation.
2. The rate of decay is constant and is not affected by temperature, pressure or chemical conditions.
3. The half-life is the time taken for half of the parent atoms in a sample to decay. After one half-life 1/2 remains, after two 1/4, after three 1/8, and so on.
4. When a rock crystallises, it traps parent atoms; from then on daughter atoms accumulate. By measuring the ratio of daughter to parent atoms, and knowing the half-life, scientists calculate the time since the rock formed.

Commonly used pairs (half-lives rounded)

• Uranium-238 to lead-206: about 4.47 billion years.
• Uranium-235 to lead-207: about 704 million years.
• Potassium-40 to argon-40: about 1.25 billion years.
• Rubidium-87 to strontium-87: about 49 billion years.
• Carbon-14 to nitrogen-14: about 5,730 years (used only for remains of once-living material up to about 50,000 years old, not for the age of the earth).

Age of the earth: the oldest rocks on earth are about 4 billion years old and some mineral grains (zircons) about 4.4 billion years; earth rocks have been recycled, so scientists also date meteorites, which formed with the solar system. These give an age of about 4.5-4.6 billion years.

Worked example

[4] Explain the principle of radioactive dating and how it gives the age of the earth. (Understanding)

Try it first, then show the solutionSolution

1. Parent isotopes decay into daughter isotopes at a constant rate - 1 mark.
2. Half-life: time for half the parent atoms to decay - 1 mark.
3. Ratio of daughter to parent in a rock gives its age (e.g., uranium-lead) - 1 mark.
4. Oldest rocks and meteorites give about 4.6 billion years - 1 mark.

Answer: Radioactive parent isotopes decay into daughter isotopes at a constant rate that is unaffected by heat or pressure; the half-life is the time for half of them to decay. Measuring the ratio of daughter to parent atoms, for example lead to uranium, in a rock and knowing the half-life gives the time since it formed. Dating the oldest earth minerals and meteorites gives the earth an age of about 4.6 billion years.

Half-life calculations

Rules
1. Fraction of parent remaining after n half-lives = (1/2)^n.
2. Time elapsed = n x half-life.
3. If the daughter-to-parent ratio is D:P (and all daughter atoms came from decay), the fraction of parent remaining = P/(P + D).

Worked illustrations

• After 3 half-lives, (1/2)^3 = 1/8 of the parent remains.
• 80 g of a radioactive element after 4 half-lives: 80 x 1/16 = 5 g.
• A rock with equal numbers of uranium-238 and lead-206 atoms (D:P = 1:1): parent fraction = 1/2, so one half-life has passed: age = 4.47 billion years.
• A mineral with argon-40 to potassium-40 ratio 3:1 (simplified): parent fraction = 1/4 = (1/2)^2, so two half-lives: 2 x 1.25 = 2.5 billion years.
• Wood with 25 per cent of its original carbon-14: 1/4 = two half-lives: 2 x 5,730 = 11,460 years.

Tip: convert the fraction into a power of 1/2 first; then multiply the number of half-lives by the half-life.

Worked example

[4] A rock contains three atoms of lead-207 for every atom of uranium-235 that remains. The half-life of U-235 is about 704 million years. (a) What fraction of the original uranium remains? (b) How many half-lives have passed? (c) Find the age of the rock. (Application)

Try it first, then show the solutionSolution

1. Parent fraction = P/(P+D) = 1/(1+3) = 1/4 - 1 mark.
2. 1/4 = (1/2)^2, so 2 half-lives - 1 mark.
3. Age = 2 x 704 million years - 1 mark.
4. = 1,408 million years (about 1.4 billion years) - 1 mark.

Answer: (a) 1/4 of the original uranium-235 remains. (b) Two half-lives have passed. (c) Age = 2 x 704 = 1,408 million years, about 1.4 billion years.

Origin and Age of the Earth in real life

Each concept, met in an everyday situation. Read the situation, answer the question in your own words, then compare with the model answer. The one-line hook is what to remember.

Topics in this chapter

• Big Bang, Nebular and Planetesimal Theories
• Radioactive Dating and Half-life Calculations

Origin and Age of the Earth: key facts

Fraction remaining

$N/N0=(1/2{)}^n,wheren=t/T$

T = half-life; t = time elapsed.

Age from fraction

$t=nxT$

Write the fraction as a power of 1/2 first.

Parent fraction from ratio

$P/(P+D)$

D = daughter atoms produced by decay.

Half-lives

U-238: 4.47 billion yr; U-235: 704 million yr; K-40: 1.25 billion yr; C-14: 5,730 yr

Rb-87: about 49 billion yr.

Key ages

Universe about 13.7 billion yr; stars 5-6 billion yr; earth about 4.6 billion yr

Oceans about 4 billion yr; life about 3.8 billion yr.

Theories

Nebular: Kant 1755, Laplace 1796; revised Schmidt and Weizsacker c.1950; Planetesimal: Chamberlin and Moulton

Big Bang: Hubble's evidence.

How the school exam asks Origin and Age of the Earth

The question patterns to expect, and the method that works for each.

Tricks to remember Origin and Age of the Earth

Short memory aids. Say each one aloud once, then use it on a question the same day.

• Big Bang order: 'Point - Pop - Particles - Galaxies - Sun'

  Singularity, expansion, atoms, galaxies and stars, solar system.

  Use it when: Stages in order.

• Who said what

  Nebula: Kant and Laplace (K-L); Planetesimal: Chamberlin and Moulton (C-M).

  Use it when: Proponents.

• Halving ladder

  1 - 1/2 - 1/4 - 1/8 - 1/16 for 0-4 half-lives.

  Use it when: Quick numericals.

Origin and Age of the Earth: exam-level solved questions

Ordered from exam level to HOTS. Cover the solution, write your own, then compare step by step.

Case-study practice (Section D style)

Read the situation, then answer every part. In a school exam set on the board pattern this is a 8-mark question split into 2 + 2 + 2 + 2 marks.

Where the marks are

How a typical answer is split into step marks. Show every step: a right final answer alone rarely earns full marks.

Where students lose marks in Origin and Age of the Earth

The slips examiners see most often, and what to write instead.

• ✗Mistake: Using carbon-14 to date the earth

  Its half-life is far too short for billions of years.

  ✓Do this: Use uranium-lead (or potassium-argon) for old rocks.

  Usually costs: 1-2 marks.

• ✗Mistake: Multiplying the ratio, not the half-lives

  Students multiply the D:P ratio by the half-life.

  Wrong working

  D:P = 3, so age = 3 x 1.25 = 3.75 billion years.

  Right working

  Parent fraction 1/4 = two half-lives; age = 2 x 1.25 = 2.5 billion years.

  ✓Do this: Find P/(P + D), express as a power of 1/2, then multiply.

  Usually costs: 2-3 marks.

• ✗Mistake: Mixing up the proponents

  Four names for two hypotheses.

  ✓Do this: Kant-Laplace: nebular; Chamberlin-Moulton: planetesimal.

  Usually costs: 1 mark.

• ✗Mistake: Calling the Big Bang an explosion in space

  It was an expansion of space itself.

  ✓Do this: Say the universe expanded from a singularity.

  Usually costs: 1 mark.

• ✗Mistake: Answers without units

  Ages need years, million years or billion years.

  ✓Do this: Always write the unit with the final age.

  Usually costs: 1 mark.

Practice questions on Origin and Age of the Earth

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

1. Q1 · 1 mark · Very short answerExam level

   About how long ago did the Big Bang take place?

   Hint

   Billions of years.

   Answer

   About 13.7 billion years ago.

2. Q2 · 1 mark · Very short answerExam level

   What is a half-life?

   Hint

   Half of the parent atoms.

   Answer

   The time taken for half of the radioactive parent atoms in a sample to decay.

3. Q3 · 1 mark · MCQExam level

   The planetesimal hypothesis was put forward by:
   (a) Kant and Laplace
   (b) Chamberlin and Moulton
   (c) Schmidt and Weizsacker
   (d) Hubble and Hoyle

   Hint

   Two Americans.

   Answer

   (b) Chamberlin and Moulton.

4. Q4 · 1 mark · Very short answerHarder exam level

   What fraction of a radioactive sample remains after four half-lives?

   Hint

   (1/2)^4.

   Answer

   1/16.

5. Q5 · 4 marks · Short answerHarder exam level

   [4] 160 g of a radioactive isotope with a half-life of 1.25 billion years is sealed in a rock. How much remains after 5 billion years, and how much has decayed?

   Hint

   Number of half-lives first.

   Answer

   (1) n = 5 / 1.25 = 4 half-lives. (2) Fraction remaining = (1/2)^4 = 1/16. (3) Remaining = 160 x 1/16 = 10 g. (4) Decayed = 160 - 10 = 150 g.

6. Q6 · 4 marks · Short answerHarder exam level

   [4] State three stages in the formation of planets according to modern theory.

   Hint

   Disc, planetesimals, accretion.

   Answer

   (1) A rotating disc of gas and dust formed around the gas core of the young sun. (2) Matter in the disc condensed into small rounded bodies, planetesimals, which grew by cohesion. (3) Planetesimals collided and, under gravity, accreted into a few large planets. (4) This combines the nebular idea of a disc with the planetesimal idea of accretion.

7. Q7 · 4 marks · Short answerHarder exam level

   [4] Why is the rate of radioactive decay a reliable clock?

   Hint

   Constant, independent, measurable.

   Answer

   (1) Each isotope decays at its own constant rate. (2) The rate is not changed by temperature, pressure or chemical reactions. (3) Parent and daughter atoms can be measured accurately in a laboratory. (4) Different isotopes with different half-lives allow dating across a wide range of ages.

8. Q8 · 4 marks · Short answerHOTS / competency

   [4] Evaluate the strengths and weaknesses of the nebular hypothesis.

   Hint

   Direction of motion; angular momentum.

   Answer

   (1) Strength: explains why planets revolve in the same direction and lie roughly in one plane. (2) Strength: its idea of a rotating disc survives in modern theory. (3) Weakness: cannot explain why the sun rotates slowly though it has most of the mass (angular momentum problem). (4) Weakness: rings of hot gas would tend to disperse rather than condense into planets.

9. Q9 · 4 marks · Short answerHOTS / competency

   [4] A mineral has a daughter-to-parent ratio of 15:1 for a parent with a half-life of 500 million years. Is it older or younger than the earth? Show working.

   Hint

   Parent fraction 1/16.

   Answer

   (1) Parent fraction = 1/(1+15) = 1/16. (2) 1/16 = (1/2)^4: four half-lives. (3) Age = 4 x 500 = 2,000 million years = 2 billion years. (4) This is younger than the earth (about 4.6 billion years), so the mineral formed long after the earth did.

10. Q10 · 7 marks · Long answerHarder exam level

    [7] (a) Explain the nebular and planetesimal hypotheses. [4]
    (b) A rock has three atoms of argon-40 for every atom of potassium-40 (half-life 1.25 billion years). Calculate its age. [3]

    Hint

    (a) two marks each; (b) fraction, half-lives, age.

    Answer

    (a) (1) Nebular (Kant, Laplace): a hot, rotating nebula cooled, contracted and spun faster. (2) Rings separated and condensed into planets; the centre became the sun. (3) Planetesimal (Chamberlin, Moulton): a passing star drew matter out of the sun. (4) The matter cooled into planetesimals that accreted into planets. (b) (1) Parent fraction = 1/(1+3) = 1/4. (2) 1/4 = (1/2)^2: two half-lives. (3) Age = 2 x 1.25 = 2.5 billion years.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1. 1.Who provided evidence that the universe is expanding?Show answer

   Edwin Hubble.

2. 2.Who revised the nebular hypothesis around 1950?Show answer

   Otto Schmidt and Carl Weizsacker.

3. 3.What is the half-life of uranium-238?Show answer

   About 4.47 billion years.

4. 4.What are planetesimals?Show answer

   Small solid bodies that collided and accreted to form planets.

5. 5.What alternative to the Big Bang did Fred Hoyle propose?Show answer

   The steady state theory.

6. 6.About how old is the earth?Show answer

   About 4.6 billion years.

Quick revision checklist

The night before the exam: can you do each of these without looking?

• ☐Big Bang: singularity; expansion 13.7 billion years ago; atoms; galaxies; stars 5-6 billion years ago; Hubble.
• ☐Nebular: Kant 1755, Laplace 1796; rotating nebula, rings to planets; angular momentum problem; Schmidt-Weizsacker c.1950.
• ☐Planetesimal: Chamberlin-Moulton; passing star; planetesimals accrete; improbable close star.
• ☐Radioactive dating: constant decay; half-life; D:P ratio; U-238 4.47 billion yr.
• ☐Fraction left = (1/2)^n; age = n x T; parent fraction = P/(P + D).
• ☐Earth about 4.6 billion years old (meteorites, oldest minerals).

Origin and Age of the Earth: frequently asked questions