Calculating natural abundance.

In summary, the conversation discusses the half-life and mean life of 244Hb, as well as the decay rate and abundance of 244Hb and 240Hb. The calculation is also used to determine the age of a sample of Hibernium, assuming there is no natural source of 244Hb.
  • #1
Eddzzz
5
0
I thought this area was appropriate for this question from a previous exam paper which I just need checking. So:

2013_02_26_22_28_17.jpg


Working out:

The half-life of 244Hb is 10 million years.
The half-life of 244Hb is 5.2595×10^12 minutes.
The mean life of 244Hb is 7.58783677×10^12 minutes.
So if you had a sample of 7.58783677×10^12 atoms of 244Hb, you could expect about 1 decay a minute.

You have x grams of 244Hb and 1-x grams of 240Hb.
Thus you have about x/244 moles of 244Hb.
Thus you have about 2.468×10^21×x atoms of 244Hb.
Since this sample decays one atom per minute, we know 2.468×10^21×x = 7.58783677×10^12.
Or x = (1/ln 2)(10 million years / 1 minute) (244 grams/mole / ( N_A per mole * 1 gram ) = 3.07×10^-9

Natural abundance of 240Hb on a per atom basis is ( x / 244)/ ( ( x / 244) + ( (1-x) / 240) ) = 60 x/(61 - x). Why?
So the natural abundance of 240Hb is about 3.02×10^-9.

If there is no natural source of 244Hb, this implies that the sample of Hibernium is no more than about 283 million years old.
 
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  • #2
Feel free to move if its in the wrong place (which I think it is!)
 
  • #3
anyone?
 

1. How is natural abundance calculated?

Natural abundance is calculated by determining the relative abundance of each isotope of an element in a sample and then converting it into a percentage. This is typically done using various analytical techniques such as mass spectrometry or nuclear magnetic resonance spectroscopy.

2. What is the purpose of calculating natural abundance?

The purpose of calculating natural abundance is to determine the relative distribution of isotopes of an element in a sample. This information can be used in various fields such as geochemistry, environmental science, and forensic science to identify the origin or source of a sample.

3. How accurate is natural abundance calculation?

The accuracy of natural abundance calculation depends on the precision and sensitivity of the analytical technique used. Mass spectrometry, for example, can accurately determine the natural abundance of isotopes to a precision of 0.001%. However, the accuracy may vary depending on the type of sample and the complexity of the isotopic distribution.

4. Can natural abundance change over time?

In most cases, natural abundance remains constant over time for a given element. However, there are some exceptions where natural abundance can change due to processes such as radioactive decay, biological fractionation, or anthropogenic activities.

5. What factors can affect natural abundance?

The natural abundance of an element can be affected by various factors such as geological processes, environmental conditions, and biological activities. Factors like climate change, pollution, and human activities can also alter the natural abundance of isotopes in the environment.

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