which isotope of which element can have its isotopic mass and mass number exactly a whole number and also have the same value for both? Give the value for the atomic mass of that element.
Answers
Answer:As mentioned above, isotopes are different forms of an element that have the same number of protons but different numbers of neutrons. Many elements—such as carbon, potassium, and uranium—have multiple naturally occurring isotopes. A neutral atom of Carbon-12 contains six protons, six neutrons, and six electrons; therefore, it has a mass number of 12 (six protons plus six neutrons). Neutral carbon-14 contains six protons, eight neutrons, and six electrons; its mass number is 14 (six protons plus eight neutrons). These two alternate forms of carbon are isotopes.
Some isotopes are stable, but others can emit, or kick out, subatomic particles to reach a more stable, lower-energy, configuration. Such isotopes are called radioisotopes, and the process in which they release particles and energy is known as decay. Radioactive decay can cause a change in the number of protons in the nucleus; when this happens, the identity of the atom changes (e.g., carbon-14 decaying to nitrogen-14).
Radioactive decay is a random but exponential process, and an isotope’s half-life is the period over which half of the material will decay to a different, relatively stable product. The ratio of the original isotope to its decay product and to stable isotopes changes in a predictable way; this predictability allows the relative abundance of the isotope to be used as a clock that measures the time from the incorporation of the isotope (e.g., into a fossil) to the present.
Graph of radioactive decay of carbon-14. The amount of carbon-14 decreases exponentially with time. The time at which half of the original carbon-14 has decayed—and half still remains—is designated as t 1/2. This time is also known as the half-life of the radioisotope and, for carbon-14, is equal to 5730 years.
Graph of radioactive decay of carbon-14. The amount of carbon-14 decreases exponentially with time. The time at which half of the original carbon-14 has decayed—and half still remains—is designated as t 1/2. This time is also known as the half-life of the radioisotope and, for carbon-14, is equal to 5730 years.
Image credit: modified from CK-12 Biology
For example, carbon is normally present in the atmosphere in the form of gases like carbon dioxide, and it exists in three isotopic forms: carbon-12 and carbon-13, which are stable, and carbon-14, which is radioactive. These forms of carbon are found in the atmosphere in relatively constant proportions, with carbon-12 as the major form at about 99%, carbon-13 as a minor form at about 1%, and carbon-14 present only in tiny amounts1^11start superscript, 1, end superscript. As plants pull carbon dioxide from the air to make sugars, the relative amount of carbon-14 in their tissues will be equal to the concentration of carbon-14 in the atmosphere. As animals eat the plants, or eat other animals that ate plants, the concentrations of carbon-14 in their bodies will also match the atmospheric concentration. When an organism dies, it stops taking in carbon-14, so the ratio of carbon-14 to carbon-12 in its remains, such as fossilized bones, will decline as carbon-14 decays gradually to nitrogen-142^22squared.
After a half-life of approximately 5,730 years, half of the carbon-14 that was initially present will have been converted to nitrogen-14. This property can be used to date formerly living objects such as old bones or wood. By comparing the ratio of carbon-14 to carbon-12 concentrations in an object to the same ratio in the atmosphere, equivalent to the starting concentration for the object, the fraction of the isotope that has not yet decayed can be determined. On the basis of this fraction, the age of the material can be calculated with accuracy if it is not much older than about 50,000 years. Other elements have isotopes with different half lives, and can thus be used to measure age on different timescales. For example, potassium-40 has a half-life of 1.25 billion years, and uranium-235 has a half-life of about 700 million years and has been used to measure the age of moon rocks2^22
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