Extinct radionuclides and the first few million years
Some radioactive isotopes present when the Solar System formed have long since decayed away. Their daughters date events in the first few million years with remarkable precision, and one of them melted the early asteroids.
- Explain how a short-lived isotope gives relative ages.
- Calculate the fraction of aluminium-26 remaining after a given time.
- Explain why asteroids that formed early melted and later ones did not.
Links to: A-level physics, radioactivity: exponential decay and half-life; links to energy release in decay.
Isotopes that have vanished
Aluminium-26 decays to magnesium-26 with a half-life of about 0.72 million years. It was present in the early Solar System but has decayed completely. Its former presence is shown by excess ²⁶Mg in aluminium-rich minerals, in proportion to their aluminium content.
Because the initial ²⁶Al/²⁷Al ratio declined with time, the ratio frozen into a mineral when it formed tells us when it formed relative to the CAIs, which have the highest ratio. Chondrules, for example, record ratios that indicate formation about 1 to 3 million years after CAIs. Other extinct isotopes, such as hafnium-182, which decays to tungsten-182 with a half-life of about 9 million years, date the formation of metal cores.
A heat source
Each ²⁶Al decay releases about 4 MeV. In the first million years, enough aluminium-26 was present in rock to release far more heat than the decay of all the long-lived isotopes combined. Bodies that assembled within roughly the first 1.5 million years, while ²⁶Al was still plentiful, heated up enough to melt and differentiate, producing iron cores and basaltic crusts. Bodies that formed later had too little ²⁶Al left to melt, and became the chondrite parent bodies, heated only enough for metamorphism.
Anchoring the timescale
Short-lived isotopes give only relative ages. To convert them to absolute ages, the same samples are dated by lead–lead, which gives an absolute age of about 4,567 million years for CAIs. Anchored in this way, the chronology shows that iron meteorite cores formed within a million or two years of CAIs, earlier than many chondrules, so melted planetesimals existed while chondrules were still forming.
How much aluminium-26 remains?
What fraction of the initial aluminium-26 (t½ = 0.72 Myr) remains after 1.5 Myr, and after 5.0 Myr?
- Number of half-lives: 1.5 ÷ 0.72 ≈ 2.08 and 5.0 ÷ 0.72 ≈ 6.94.
- Fraction remaining = (1/2)^n.
- After 1.5 Myr: 2^(−2.08) ≈ 0.24.
- After 5.0 Myr: 2^(−6.94) ≈ 0.0082.
Answer: About 24% after 1.5 Myr, but under 1% after 5 Myr. A body that formed 5 Myr after CAIs had about thirty times less heat source than one formed at 1.5 Myr, which is why late-forming bodies stayed unmelted.
Plot the fraction of aluminium-26 remaining against time from 0 to 6 Myr. Mark on your graph when CAIs formed, when most chondrules formed (1 to 3 Myr) and when the parent bodies of iron meteorites formed (within about 1.5 Myr). Write a paragraph explaining which bodies melted and which did not.
Quiz
5 questions. Choose an answer to see whether you are right and why. Finish the quiz to complete the lesson.
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Question 1How is the former presence of aluminium-26 detected?
²⁶Al decayed to ²⁶Mg, so aluminium-rich minerals carry extra ²⁶Mg in proportion to their Al/Mg ratio.
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Question 2Why can extinct radionuclides only give relative ages on their own?
They show how much time passed after the CAIs; anchoring to lead–lead dating converts this to absolute ages.
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Question 3What fraction of ²⁶Al remains after 2.16 Myr (3 half-lives)?
(1/2)³ = 1/8.
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Question 4Why did early-forming planetesimals melt while later ones did not?
The heat available depended on how much ²⁶Al remained when a body assembled.
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Question 5What does the Hf–W system mainly date?
Hafnium stays in rock while tungsten enters metal, so ¹⁸²W anomalies record when metal separated into cores.