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Atomic Structure

>> Parts of this equation/concept include:

A -	Determining the Number of Protons, Neutrons, and Electrons in an Atom
B -	Average Atomic Mass

The periodic table is an invaluable tool for determining the characteristics of an atom. Each block of the periodic table contains, at a minimum; the symbol representing the identity of the element, the atomic number of the element, and the average isotopic mass of the element. The symbol is an uppercase letter or an uppercase and a lowercase letter corresponding to the name of the element (although sometimes not the English name). The atomic number is the whole number that is sequential across the table. The average atomic mass is the fractional value.

The number of protons of an element is the same value as its atomic number. In atoms, which are electrically neutral, the number of electrons is the same as the number of protons. For ions, the number of protons and the number of electrons are not the same. The number of neutrons depends on the type of isotope. Since the periodic table gives only the average mass, it cannot be used to determine the number of neutrons. However, the mass number, which is the sum of the protons and neutrons, is included as a superscript before the chemical symbol. A reasonable guess for the mass number of the most abundant isotope is to round the average atomic mass to the nearest whole number.

To summarize, for an isotope of ^AE, where A is the mass number and E is the symbol of the element, the number of protons and the number of electrons are equal to the atomic number, Z, and the number of neutrons is A – Z.

Hint: No one takes that periodic table off the wall of the classroom, so don't bother to memorize it. Since not all periodic tables have the name of the element, it is worthwhile to memorize the names that go with each symbol for the common elements. If you learn the first 20 or 30, you'll pick up the other common ones quickly.

>> Example 1

How many protons, neutrons, and electrons are in the following isotopes?

1. ³H
2. ¹¹²Cd
3. ³⁷Cl
4. ¹⁶O

Solution:

1. Hydrogen has an atomic number of 1. So p = 1, e = 1, and n = 3 – 1 = 2.
2. Cadmium is atomic number 48. So p = 48, e = 48, and n = 112 – 48 = 64.
3. Chlorine is atomic number 17. So p = 17, e = 17, and n = 37 – 17 = 20.
4. Oxygen is element 8. So p = 8, e = 8, and n = 16 – 8 = 8.

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The average atomic mass takes into account both the mass of each naturally occurring isotope and the percentage of that isotope in a large sample. These values are experimentally determined, so they must be given as part of the problem.

To determine average atomic mass, change the percentage to the corresponding fraction and multiply by the mass of that isotope; add all these products together.

The mass number is the number of protons + neutrons; it is not the actual mass of the atom. However, if that is all the information you have, it is a good estimate.

>> Example 2

What is the average atomic mass of lead if its isotopic abundance is 1.4% ²⁰⁴Pb, 24.1% ²⁰⁶Pb, 52.4% ²⁰⁸Pb, and 22.1% ²⁰⁷Pb?

Solution:

Assume the mass number is the mass of the atom (at least until the first decimal place). The fraction of the average mass due to that isotope is that fraction times the mass number. Therefore

average mass	= 0.014(204) + 0.241(206) + 0.524(208) + 0.221(207)
	= 2.856 + 49.646 + 108.992 + 45.747
	= 207.241 amu
	= 207 amu

>> Example 3

What is the average atomic mass of gallium, which has two isotopes, 60.0% ⁶⁹Ga (actual mass = 68.9256) and 40.0% ⁷¹Ga (actual mass = 70.9247)?

Solution:

average mass	= 0.600(68.9256) + 0.400(70.9247)
	= 41.35536 + 28.3699
	= 69.72524 amu
	= 69.7 amu

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