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How many years will it take for Carbon-14 to diminish to 1% of the original amount after the death of a plant or animal? Use the formula A = Ao e (-0.000124t). Compute the answer to three signiﬁcant digits.
The time taken by Carbon-14 to diminish to 1% of the original amount after the death of a plant or animal
You could have seen or read news stories giving details about ancient artifacts. A group of archaeologist conducting an archaeological research in a particular place unearth a piece of wooden tool and report that the wooden tool is 5000 years old. Have you ever thought how do archaeologists know how old an object is? What technique or method they could have used to find out the age of the object? The answer to these questions is quite simple. It is through Carbon-14 dating, archaeologists find the age of an object. Where does this carbon -14 come from? We shall see it in detail now.
Cosmic rays enter the earth's atmosphere and they collide with other atoms in the atmosphere creating secondary cosmic rays in the form of energetic neutrons. These energetic neutrons collide with a nitrogen-14 atom and form carbon-14 atom and a hydrogen atom. The carbon-14 atom has half-life of about 5700 years. But the question now is how these carbon-14 atom help in finding the age of an object.
Carbon-14 atoms play a very important role in living organisms. The carbon-14 atoms created by cosmic rays combine with oxygen and form carbon dioxide, which is absorbed by plants and are incorporated into plant fibers by photosynthesis. Animals and humans eat these plants and take in carbon-14 atoms. It should be noted here that the ratio of normal carbon i.e. carbon-12 to carbon-14 in all living things and in air at any given time is nearly constant. And another point to be considered it that carbon-14 atoms are always decaying and are replaced by new carbon-14 atoms at a constant rate. So, at this moment there is a certain amount of carbon-14 atoms present in our body as well as in all living plants and animals.
However the percentage decreases when the organism dies, because when the organism dies new carbon -14 atoms are not absorbed and carbon -14 atoms present in them keep on decreasing. Now the ratio of carbon-12 to carbon-14 is also not a constant, because carbon -14 is decaying at its half-life of 5700 years and not replaced, and carbon-12 remains constant in the organism. By comparing the ratio of carbon-12 to carbon-14 in the sample to the ratio in a living organism, we can determine the age of the sample.
The formula that is used to find age is,
A is the number of grams of carbon -14 at the present time
A0 is the number of grams of carbon -14 while alive
t is the number of years since death
Now by using the formula stated above, we can determine time taken by carbon-14 to diminish to 1% of original amount after the death of a plant or animal.
In the problem it has been stated that carbon -14 is diminishing by 1% from original amount. So, amount of carbon -14 present when the organism was alive (A0) is 1%.
The amount of carbon -14 at present is given by,
Now by substituting the values we get,
Now solving for t we get,
Therefore, the time taken by carbon-14 to diminish to 1% of the original amount after the death of a plant or animal is 35.161 years.
Protein A has a binding site for ligand X with a Kd of 10-6M. Protein B has a binding site for ligand X with a Kd of 10-9M. Which protein has the higher affinity for ligand X?
Dissociation constant (Kd) for protein A = 10-6M
Dissociation constant (Kd) for protein B = 10-9M
The affinity of proteins towards ligand X
Proteins are large and complex biomolecules made up of chains of amino acids. The amino acids are bonded by peptide bonds, and they can take on a variety of complicated shapes. Proteins can bond with other molecules such as ligands, or even other proteins, at particular sites known as binding sites. The binding sites have indentations into which ligands can neatly fit. The binding of the protein to ligands occurs only when they are chemically feasible. The chemical properties of the binding site and ligand are very important when binding occurs.
Let us consider hemoglobin protein. Hemoglobin protein consists of 4 binding sites into which only oxygen molecules fit in. The function of hemoglobin is to transport oxygen from the lungs to other parts of the body. Hemoglobin acts as a vehicle in transporting oxygen. Once the oxygen molecules bind to hemoglobin protein they move to various parts of our body, where oxygen is required. Although hemoglobin is chemically feasible to oxygen, the bond formed between them is weak because oxygen must be easily removed from the protein when it is needed.
Each and every protein has affinity to bind to other molecules, but there degree of affinity differs according to the structure, chemical properties, functions, etc. This is defined by association constant (Ka). Association constant provides a measure of affinity of the ligand for the protein. Higher the value of Ka, higher is the affinity of ligand for the protein. Association constant is given by,
Where, Kd is the dissociation constant. Dissociation constant describes the affinity between a ligand and a protein i.e. how tightly a ligand binds to a particular protein.
The task is to find out which protein has higher affinity for ligand X. It has been stated that protein A has a binding site for ligand X with a dissociation constant (Kd) of 10-6M, and protein B has a binding site for ligand X with a dissociation constant (Kd) of 10-9M. By calculating the association constant (Ka) for both the proteins, we will be able to determine which protein has higher affinity for ligand X.
The association constant (Ka) values calculated for the proteins clearly shows that Protein B has a higher affinity for ligand X.
What is the effect of the following changes on the O2 affinity of hemoglobin? (a) A decrease in the blood pH from 7.4 to 7.2. (b) A decrease in the partial pressures of CO2 in the lungs from 6 kPa (holding one's breath) to 2 kPa (normal). (c) An increase in the BPG level from 5 mM (normal altitudes) to 8 mM (high altitudes). For (c), also consider fetal hemoglobin.
Change in blood pH = 7.4 to 7.2
Change in partial pressures of CO2 = 6 kPa to 2 kPa
Change in BPG level = 5 mM to 8 mM
The O2 affinity of hemoglobin when there are changes in blood pH, partial pressures of CO2 in the lungs and BPG level
While solving problem 2, we learnt that hemoglobin protein has strong affinity for oxygen molecules and they bind to the protein at 4 specific binding sites. In addition to oxygen molecules, some ligands also bind to hemoglobin, which bring about direct effects in the O2 affinity of hemoglobin. The O2 affinity of hemoglobin can be easily understood by using the O2 – Saturation Curve (figure)
The binding of ligands to hemoglobin shifts the O2-saturation curve to the right, showing that O2 affinity of hemoglobin is reduced in the presence of ligand. When ligands like hydrogen ions (H+), carbon dioxide (CO2) and Bisphosphoglycerate (BPG) bind to hemoglobin they decrease O2 affinity.
(a) Let us consider the first case, where blood pH is decreased from 7.4 to 7.2. When the level of carbon dioxide is high, it lowers blood pH value making it more acidic. So, in this situation protons and carbon dioxide bind to hemoglobin and a conformational change occurs in the protein facilitating the release of oxygen. This decreases the affinity for oxygen in hemoglobin by the binding of carbon dioxide. So, when blood pH is decreased from 7.4 to 7.2, a large amount of carbon dioxide (CO2) ligands bind to hemoglobin, thereby decreasing O2 affinity of hemoglobin.
(b) In the second case, the partial pressure of CO2 in the lungs is deceased from 6 kPa (holding one's breath) to 2 kPa (normal). When the level of CO2 in the blood is decreased, CO2 and protons bound to the hemoglobin are released favoring the binding of oxygen molecules to hemoglobin protein, which results in increasing O2 affinity of hemoglobin.
(c) Let us consider the last case, where BPG level is increased from 5 mM (normal altitudes) to 8 mM (high altitudes). When BPG level is increased BPG ligands bind to hemoglobin thereby decreasing O2 affinity of hemoglobin. These effects can also be directly inferred from the O2 – Saturation Curve given above.
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