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Atomic Weights and Isotopes
To report the mass of something, one generally gives a number together with a unit like pounds, kilograms (kg), grams (g), etcetera. Because the mass of an atom is so small, however, these units are not very convenient, and new ways have been devised to describe how much an atom weighs. A unit that can be used to report the mass of an atom is the atomic mass unit (amu). One amu is approximately the same as 1.66 x 10-24 g. How is this particular value chosen? Why not, for example, have 1 amu be equal to a nice round number like 1.00 x 10-24 g instead? The answer is that it is chosen so that a carbon-12 atom, with 6 protons and 6 neutrons, will have a mass of 12 amu. In other words, the amu is defined as one-twelfth the mass of the carbon-12 atom. It does not convert nicely to grams because the mass of a carbon-12 atom in grams is not a nice round number. In addition, since the mass of an electron is negligible, all the mass of the carbon-12 atom is considered to come from protons and neutrons.
Since the mass of a proton is about the same as that of a neutron, and there are 6 of each in the carbon-12 atom, protons and neutrons are considered to have a mass of 1/12 x 12 amu = 1 amu each.
While it is necessary to have a way of describing the weight of an individual atom, in real life one generally works with a huge number of them at a time. The atomic weight is the mass in grams of one mole (mol) of atoms. Just like a pair corresponds to two, and a dozen corresponds to twelve, a mole corresponds to about 6.022 x 1023. The atomic weight of an element, expressed in terms of g/mol, therefore, is the mass in grams of 6.022 x 1023 atoms of that element. This number, roughly 6.022 x 1023, to which a mole corresponds, is known as Avogadro's number. Why this particular value and not something like 1.0 x 1024, for example? Once again, the answer lies in the carbon-12 atom: a mole of carbon-12 atoms weigh exactly 12 g. In other words, a mole is defined as the number of atoms in 12 g of carbon-12. A mole of atoms of an element heavier than carbon-12 (such as oxygen) would have an atomic weight higher than 12 g/mol, while a mole of atoms of an element lighter than carbon-12 (such as helium) would have an atomic weight less than 12 g/mol. Six g of carbon-12 would mean 3.011 x 1023 cabon-12 atoms, etcetera.
As we have seen, Avogadro's number serves as a conversion factor between one of something and a mole of something. Since 12 amu is the mass of I carbon-12 atom while 12 g is the mass of 1 mole of carbon-12 atoms, Avogadro's number also helps to convert between the mass units. Specifically:
12 amu x (6.022 x 1023) = 12 g
1 amu = 1/6.022 x 1023 = 1.66 x 10-24 g
which is the conversion factor we gave above. We can now see how this is derived from (or related to) the concept of the mole.
The atomic weight of an element is also found in the Periodic Table, as the number appearing below the symbol for the element. Notice, however, that these numbers are not whole numbers, which is odd considering that a proton and a neutron each have a mass of 1 amu and an atom can only have a whole number of these. Furthermore, even carbon, the element with which we have set the standards, does not have a mass of 12.000 exactly. This is due to the presence of isotopes, as mentioned above. The masses listed in the Periodic Table are weighted averages that account for the relative abundance of various isotopes. The word weighted is important: It is not simply the average of the masses of individual isotopes, but takes into account how frequently one encounters that isotope in a common sample of the element. There are, for example, 3 isotopes of hydrogen, with 0, 1, and 2 neutrons respectively. Together with the one proton that makes it hydrogen in the first place, the mass numbers for these isotopes are 1, 2, and 3. The atomic weight of hydrogen, however, is not simply 2 (the average of 1, 2 and 3) but about 1.008, that is, much closer to 1. This is because the isotope with no neutrons is so much more abundant that we count it much more heavily in calculating the average. The following example provides a more concrete illustration of the idea.
Example: Element Q consists of three different isotopes, A, B, and C. Isotope A has an atomic mass of 40 amu and accounts for 60% of naturally occurring Q. The atomic mass of isotope B is 44 ainu and accounts for 25% of Q. Finally, isotope C has an atomic mass of 41 amu and a natural abundance of 15%. What is the atomic weight of element Q?
0.60(40 amu) + 0.25(44 amu)
= 24.00 amu + 11.00 amu + 6.15 amu = 41.15 amu
The atomic weight of element Q is 41.15 g/mol.
(Incidentally, if you have studied physics, you may be aware of the distinction between mass and weight. As you can see, chemists are a bit sloppier on this matter.)
Bohr's Model of the Hydrogen Atom
In his model of the structure of the hydrogen atom, Bohr postulated that an electron can exist only in certain fixed energy states; the energy of an electron is "quantized." According to tiffs model, electrons revolve around the nucleus in orbits. The energy of the electron is related to the radius of its orbit: The smaller the radius, the lower the energy state of the electron. The smallest orbit (radius) an electron can have corresponds to the ground state of the hydrogen electron. At the ground state level, the electron is in its lowest energy state. The fact that only certain energy values are allowed means that only certain orbit sizes are allowed.
The Bohr model is used to explain the atomic emission spectrum and atomic absorption spectrum of hydrogen. Since the energy of electrons can only take on certain values, the energy an atom can emit or absorb is likewise restrained to values that correspond to differences between these levels. When a hydrogen atom absorbs energy in the form of radiation, for example, its electron moves to a higher energy level. When such a process occurs, a peak shows up in the absorption spectrum, signifying that radiation of that particular energy is being absorbed by the atom. The crucial thing to realize is that there will only be a certain number of sharp peaks, corresponding to energy values that match up with the difference between energy levels. The principle behind the emission spectrum is the same: The atom gives off energy as an electron goes from a higher to a lower energy level, and this will show up as distinct peaks in a spectrum corresponding to transition between different levels. The Bohr model successfully accounted for the precise positionings of these peaks (the precise values of the energy that can be emitted).
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