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Atomic number, atomic mass, and isotopes

Fundamental properties of atoms including atomic number and atomic mass. The atomic number is the number of protons in an atom, and isotopes have the same atomic number but differ in the number of neutrons.


Radioactivity pops up fairly often in the news. For instance, you might have read about it in discussions of nuclear energy, the Fukushima reactor tragedy, or the development of nuclear weapons. It also shows up in popular culture: many superheroes’ origin stories involve radiation exposure, for instance—or, in the case of Spider-Man, a bite from a radioactive spider. But what exactly does it mean for something to be radioactive?
Radioactivity is actually a property of an atom. Radioactive atoms have unstable nuclei, and they will eventually release subatomic particles to become more stable, giving off energy—radiation—in the process. Often, elements come in both radioactive and nonradioactive versions that differ in the number of neutrons they contain. These different versions of elements are called isotopes, and small quantities of radioactive isotopes often occur in nature. For instance, a small amount of carbon exists in the atmosphere as radioactive carbon-14, and the amount of carbon-14 found in fossils allows paleontologists to determine their age.
In this article, we’ll look in more detail at the subatomic particles that different atoms contain as well as what makes an isotope radioactive.

Atomic number, atomic mass, and relative atomic mass

Atoms of each element contain a characteristic number of protons. In fact, the number of protons determines what atom we are looking at (e.g., all atoms with six protons are carbon atoms); the number of protons in an atom is called the atomic number. In contrast, the number of neutrons for a given element can vary. Forms of the same atom that differ only in their number of neutrons are called isotopes. Together, the number of protons and the number of neutrons determine an element’s mass number: mass number = protons + neutrons. If you want to calculate how many neutrons an atom has, you can simply subtract the number of protons, or atomic number, from the mass number.
A property closely related to an atom’s mass number is its atomic mass. The atomic mass of a single atom is simply its total mass and is typically expressed in atomic mass units or amu. By definition, an atom of carbon with six neutrons, carbon-12, has an atomic mass of 12 amu. Other atoms don’t generally have round-number atomic masses for reasons that are a little beyond the scope of this article. In general, though, an atom's atomic mass will be very close to its mass number, but will have some deviation in the decimal places.
Since an element’s isotopes have different atomic masses, scientists may also determine the relative atomic mass—sometimes called the atomic weight—for an element. The relative atomic mass is an average of the atomic masses of all the different isotopes in a sample, with each isotope's contribution to the average determined by how big a fraction of the sample it makes up. The relative atomic masses given in periodic table entries—like the one for hydrogen, below—are calculated for all the naturally occurring isotopes of each element, weighted by the abundance of those isotopes on earth. Extraterrestrial objects, like asteroids or meteors, might have very different isotope abundances.
Image credit: modified from OpenStax CNX Biology

Isotopes and radioactive decay

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.
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. 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.
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.

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  • leaf red style avatar for user Annemarie
    So for radiometric rating to work, you have to assume that the element has been decaying at the same rate the entire time?
    (35 votes)
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    • leafers ultimate style avatar for user Miguel Angelo Santos Bicudo
      @Sean Collin: the amount of carbon isotopes can be determined for each geologic era by analyzing glaciers, because they imprison atmospheric gases. The geologic era can be determined by the depth of the extracted sample from the ice, because the rate at which it forms is predictable. That can also be done with other kinds of natural formations such as rocks, soil, and anything that captures carbon atoms, and that have predictable rates of formation.
      (35 votes)
  • starky ultimate style avatar for user Thanaa'
    How did they know that it takes 5730 years for it to decay? How can we measure such a thing?
    (10 votes)
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    • male robot hal style avatar for user Charles LaCour
      The half-life of carbon 14 is 5730 years, this means that 50% of it will undergo radioactive decay in 5730 years. Or another way of looking at it a single atom of C14 has a 50% chance of undergoing radioactive decay in 5730 years.

      The decay of an individual atom of c14 is random so if you have 12 grams of carbon 14 you have about 6 * 10^23 atoms so there will be some that decay within seconds and other that will decay in 10,000 of years. We know that the rate of decay is random but on average a constant so if 3*10^23 atoms in the 12 grams will decay in 5730 years we know that 5*10^19 will decay in a year or 1.62*10^12 atoms decaying in a second.

      This rate is measurable and from the decay rate you can determine the half life.
      (18 votes)
  • blobby green style avatar for user sabin  thapa
    so if the atomic number of a element is given you know what the proton is; the same as the atomic number. if that element is neutral you also know that the number of electrons is the same. but if you are only given the atomic number is it possible to find out what the atomic mass is?
    (3 votes)
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    • piceratops ultimate style avatar for user Just Keith
      No. The atomic mass is a laboratory-measured value, so you cannot determine it from the atomic number.

      You can approximate the atomic mass of a single isotope (not the element in general) by guessing that the atomic mass in atomic mass units is numerically the same as the mass number (the number of protons + the number of neutrons). However, that is only an approximation.
      (21 votes)
  • blobby green style avatar for user Pharm
    How is possible carbon 14 atom convert to nitrogen 14 gradually ? I thought that can not be possible and if it does i guessed somehow in years the carbon can convert to some elements which has less proton numbers not opposite way
    (6 votes)
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  • male robot donald style avatar for user Angel Mihail
    There is any better way to find the age of a very very old object ?? Like with what we mesure if carbon- 14 ,potassium-40 and uranium-235 concentration test fails ? And one more question: how accurate those carbon dating is? Can the fossils be infested whit those isotopes when the test is made ?
    (2 votes)
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  • starky ultimate style avatar for user Jason_Cow
    If everything is actually 99.99% empty space, that means that the ground is too... Why aren't we falling through all that empty space? Also, If everything is 99.99% empty space, why can we only feel the NOT empty space?
    (8 votes)
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  • eggleston blue style avatar for user wonuuu
    How do you compute for their half-life?
    (6 votes)
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    • male robot hal style avatar for user 𝕲𝖊𝖔𝖗𝖌𝖊
      You can refer to the answer by Charles LaCour - it basically states that by measuring the rate of decay at smaller amounts of time, we can leverage the fact that the rate of decay is often a constant (a certain number of atoms decays within a certain amount of time). Then, we can use this constant to apply to larger amounts of time, finding the half-life of a complete sample.

      Mathematically, you can use the half-life formula to determine the half-life period:

      N(t) = N0 * (1/2) ^ (t/h), where
      N(t) is the amount remaining,
      N0 is the original amount,
      t is the time elapsed,
      and h is the half-life period.

      You can rearrange the variables to solve for the half-life.
      (5 votes)
  • leafers tree style avatar for user Jacob Snyder
    Why is carbon 14 sometimes radioactive?
    (5 votes)
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  • old spice man blue style avatar for user Ramon Galarza
    How do you calculate the natural abundance of an isotope?
    (3 votes)
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  • aqualine ultimate style avatar for user zalexan1
    So when someone says they carbon date a fossil and say it is 1 billion years old, because C-14 has a half-life of 5,730 years, they used K-40 and not C-14?
    (4 votes)
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