Universe: Stars And Galaxies
Universe: Stars And Galaxies
6th Edition
ISBN: 9781319115098
Author: Roger Freedman, Robert Geller, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 19, Problem 16Q
To determine

The way the universe would have been different if the half-life of

8Be was zero and if it was stable.

Expert Solution & Answer
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Answer to Problem 16Q

If the half- life of 8Be was not zero the universe would be richer with atoms other than Hydrogen and Helium, but zero half- life of 8Be prevents the process. If the 8Be nucleus was stable, 12C and organic molecules would form life in other planets as well.

Explanation of Solution

Given:

The half- life of 8Be is 2.6×1016seconds.

8Be decays in to two α particles.

Formula used:

The half- life equation,

A=A0×[12]thWhere, A= Final amount of particles, A0=Initial amount of partclies, t= time and h= half- life

Calculation:

Analyzing the two situations where the half-life of 8Be was zero and 8Be nucleus was stable.

For zero half- life, h=0. Then,

A=A0×[12]t0A=A0×[12]A=A0×0A=0

This means 8Be decays extremely faster, even faster than 2.6×1016seconds.

If 8Be nucleus was stable and did not decay, then the half- life is .

For half- life, h= . Then,

A=A0×[12]tA=A0×[12]0A=A0×1A=A0

The final amount of particles is the same as the initial amount. The result implies that 8Be nucleus is extremely stable and exists.

Be is the fourth element in the periodic table and a solid at room temperature. It has four protons and five neutrons in its nucleus. Be has many known isotopes and 8Be is one of them. All those isotopes have different decaying paths while 8Be decays into two α particles.

Most of the elements having a similar number of protons and neutrons are stable especially if the number of protons is even. 8Be also has four protons and four neutrons. According to the above description 8Be should be stable. However, the half-life of 8Be isotope is extremely low ( 2.6×1016seconds ) leaving it heavily unstable. Due to this reason 8Be is non- existent.

An α particle is equivalent to a Helium- 4 nuclei. Inside a star after the Hydrogen fusion, Helium fusion begins, producing elements heavier than Helium which means Helium fuses in to 8Be. But due to the very low half-life, 8Be decays instantly back into two α particles.

In a core of a star with enough pressure and mass, two α particles can collide to form 8Be and within its very short lifespan another α particle can hit it forming a 12C which is stable. If this happens future stars might consist Be and heavier elements. Then the universe would be richer with other atoms as well instead of only Hydrogen and Helium. Having intensively low half-life would stop this process leaving Hydrogen and Helium be the only elements left in the cosmos.

On the other hand, if 8Be was extremely stable and did not decay which means having an extremely high half- life, even smaller stars could produce heavier elements including 8Be .Since Be is solid at room temperature, most of the planets would consist denser rocks. Stable 8Be would lead to form 12C easier which then leads to form organic molecules as well. Thus life could be formed in many planets in the universe.

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