--------------------- #1515 - How old is that star? How do we know?
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- Astronomers can learn the age of a star by measuring the abundance of a radioactive element isotope and knowing the ½ life of its radioactive decay.
- The most ancient stars were only composed of hydrogen ,helium, and a small amount of lithium. The heavier elements in the periodic table were only formed in the nuclear fusion process of these stars. The early stars in the Universe were massive, 10 to 100 times more massive than our Sun. These massive stars and enormous gravity that burned through their nuclear fuel relatively quickly. Their lifetimes were in the 10s of millions of years. In contrast, our Sun of one Solar Mass will live 1,000 times longer to 10 billion years of age.
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- When massive stars end their lifetimes they explode in giant supernovae spreading the newly created heavier elements into the interstellar medium.
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- The next generation of stars that form from this interstellar medium have compositions that include these heavier elements. Each generation of stars accumulates more of the heavier element.
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- For example, when astronomers used spectroscopy to measure the element Uranium-238 in the Cayrel’s Star they found the abundance of the radioactive to be only 14.3% compared to our Sun that was found to have 50% of its Uranium-238 that had not decayed.
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- Our Sun is 4.6 billion years old. Cayrel’s Star must be much older because much more of its radioactive element U-238 has decayed.
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- The half-life of U238 is known to be 4.47 billion years ( t½)
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- The decaying process follows a exponential function given by the following function.:
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-------------- The ratio of the current abundance of the element (N) to the initial abundance of the element (n) = e^ -0.69 ( T / t½). Where “T” is the elapsed time (T).
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------------------------ N / n = e^ -0.69 ( T / t½).
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- In the case of Cayrel’s Star we have determined the abundance “N/n” to be 14.3% left that has not decayed. N/n = 0.143
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------------------------ t½ = 4.47
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------------------------ Solving for “T”
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--------------------- 0.143 = e^ -0.69 ( T/4.47)
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---------------------- Taking the natural log of both sides of the equation:
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----------------------- Log e ( 0.143) = -0.69 ? T/4.47)
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---------------------- - 1.95 = -0.154 * T
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---------------------- T = 12.66 billion years
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- The age of Cayrel’s Star must be 12.7 billion years. The Universe is 13.7 billion years. This star was born when the Universe was only 1 billion years old.
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- If we know the age and want to calculate the relative abundance of U-238. We can use the same equation for our Sun.
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------------------------ N / n = e^ -0.69 ( T / t½).
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- ---------------------- N/n = ?
----------------------- T = 4.6 billion years
---------------------- t ½ = 4,47 billion years.
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------------------------ N / n = e^ -0.69 ( 4.6 / 4.47).
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------------------------ N/n = e^ -0.71
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------------------------- N/n = ½
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- There are 50% as many atoms of U-238 today as there were when the Sun was formed 4.6 billion years ago.
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(1) Cayrel’s Star is in the Constellation Cetus the Whale. It is 13,000 lightyears away. This calculation of its age was made in 2001.
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