III. Isotopes and Atomic Mass

For example, most of the oxygen atoms in nature have eight neutrons in their atomic nuclei. In other words, most oxygen atoms have a mass number of 16 (8 protons +8 neutrons). However, there are also two other naturally occurring forms of oxygen. One of these has nine neutrons, so A=17. The other has ten neutrons, so A=18. These three forms of oxygen are called isotopes.

The isotopes of an element have very similar chemical properties because they have the same number of protons and electrons. They differ in mass, however, because they have different numbers of neutrons.

2. Atomic mass (atomic weight) of an element is the number of times an atom of that element is heavier than an atomic mass unit.

The atomic mass unit (amu), which is represented with the symbol “u,” is based on a particular isotope of carbon, called carbon-12. Carbon-12 is considered to have a mass of exactly 12 u, and all of the other elemental isotopes are measured relative to that isotope. The atomic masses, shown on the periodic table, represent a weighted average of the masses of the naturally occurring isotopes of each element. For example, some periodic tables show an atomic mass of 1.00794u for hydrogen, despite the fact that no particular isotope of hydrogen has a mass number equal to that value. Chemists come up with an average, based on the mass numbers of the isotopes and the relative abundance by which they appear. The fact that the atomic number of hydrogen is so close to the mass number of the isotope of hydrogen known as protiumindicates that the vast majority of the hydrogen atoms found in nature (approximately 99%) are of this type.

3. Average Atomic Mass

The average atomic mass of an element is the average of the masses of all the element’s isotopes. It takes into account the abundance of each isotope within the element. The average atomic mass is the mass that is given for each element in the periodic table.

For example, lithium exists as two isotopes: lithium-7 and lithium-6, lithium-7 has a mass of 7.015 u and makes up 92.58% of lithium. Lithium-6 has a mass of 6.015 u and makes up the remaining 7.42%. To calculate the average atomic mass of lithium, multiply the mass of each isotope by its abundance.

92.58%x7.015u + 7.42%x6.015u = 6.94u

IV. Quantum Numbers

Compared to the old planetary model of the atom, the quantum-mechanic model seems much less certain. Instead of thinking of electrons as occupying fixed orbits with predictable paths, we now think in terms of probability. Although you shouldn’t think of the electrons as being locked into fixed orbits, the way planets are, we are able to predict the areas where electrons are most likely to be found. Imagine that you needed to find your chemistry teacher outside of class, perhaps to give him or her a lab report. You might start by going to the floor of the building where the science classes are found. You might then narrow your search to the specific hallway in which the classroom is located. You might then check in the specific classroom. Your teacher might not be in that classroom, but this may be the place where he or she probably is.

Our model of the electron cloud is broken up into areas, as in the example of finding the chemistry teacher. Each electron is located in a specific energy level (in our example, the floors of a building). Each energy level is broken up into sublevels (the different hallways on the floor of a building). Each sublevel contains a certain number of orbitals (just as a hallway can contain some number of rooms).

Just as levels of a building are given numbers, energy levels are given numbers as well. As a floor, or level of a building, can contain several hallways, each energy level is broken up into sublevels, which are designated by specific letters. Each sublevel can contain a certain number of orbitals, which are analogous to the rooms in the hallway. Each orbital can contain up to two electrons.

The rooms in many buildings contain numbers on their doors, so that they can be found easily. So to, numbers are given to electrons, so that we can picture where they are likely to be found. The numbers that are given to electrons are called quantum numbers, and each electron is given four.

1. Principal Quantum Number (n): The principal, or first, quantum number is used to indicate the energy level that the electron is found in. The value for n will always be a whole number, and the higher the number, the further away from the nucleus the electron described by n tends to be. For example, an electron with a value of 3 for n is in the third energy level, so it is likely to be located further away from the nucleus than an electron with a value of 1 for n.

Each energy level is divided into sublevels, the number of which is equal to the value of n. So, for example, the third energy level (n = 3) contains 3 sublevels, whereas the fifth energy level (n = 5) would contain 5 sublevels.

The smaller n is the lower the energy. For other atoms, the energy also depends to a slight extent on the l quantum number. The size of an orbital also depends on n. The larger the value of n is, the larger the orbital. Orbitals of the same quantum state n are said to belong to the same shell. Shells are sometimes designated by the following letters:

Letter K L M N . . .

n 1 2 3 4 . .

(Also Called Azimuthal Quantum Number)

This quantum number distinguishes orbitals of given n having different shapes; it can have any integer value from 0 to n 1. The second quantum number, called the angular momentum quantum number, is used to indicate the type of sublevel that the electron occupies. The possible values for l refer to the types of sublevels, each of which contain a certain number of orbitals. An orbitalis a space that can be occupied by up to two electrons, which occupy a specific three dimensional area. Depending on the course that you are in, you may or may not need to know the shapes of the sublevels, but you are very likely to need to know the number of orbitals and electrons that each one holds. Values of l of 0, 1, 2, and 3 refer to sublevels, which are, in turn, designated by the letters s, p, d, and f respectively. So, an electron that has a value 3 for n (the first quantum number) and a value of 1 for l (the second quantum number) would be found in the third energy level, in a “p” sublevel.

3. The total number of electrons that an energy level

Each orbital can hold up to two electrons, so a p sublevel, which contains 3 orbitals, can hold up to 6 electrons (2 electrons × 3 orbitals). To find out how many total electrons a certain energy level can hold, you can do one of two things. First, you could add up the total number of electrons that each of its sublevels can hold. For example, the fourth energy level has four sublevels (s, p, d, and f), which-hold 2, 6, 10, and 14 electrons respectively. We can add these numbers together to find that the fourth energy level can hold 32e^- (2 + 6 + 10 + 14 = 32). Another way to calculate the total number of electrons that an energy level can hold is to use the formula 2n² , where n is the energy level number. Solving for n = 4, we find that 2(4)² = 32 e^-.

The information that we have covered on quantum numbers will be used to construct a type of notation called the electron configurations of elements.

V. Electron Configuration

1. Valence electrons: The electrons in the highest energy level, which are called valence electrons, are probably the most important part of the atom. It is these electrons that determine the reactivity of an element. When we talk about electron configuration, we are speaking of the arrangement of the electrons in a particular atom or element. By being able to determine these arrangements, you will be able to predict how an element reacts with other elements and what types of compounds it will form. We will start by learning how to read an electron configuration.

Look at the electron configuration for hydrogen H: 1s¹.

The superscript shows us that hydrogen has only one electron. The large (coefficient) number represents the principal quantum number for the electron. In this case, because the value for n = 1, it means that this electron is located in the first energy level. The letter indicates the sublevel that the electron is located in. Because there is only one energy level in this particular atom, it represents the valence shell, or outer energy level. Hydrogen is said to have one electron in its valence shell.

The Electron Configuration of Oxygen: 1s²2s²2p⁴

First add up the superscripts and you will see that there are a total of 8 electrons (2+2+4 = 8). This makes sense, because oxygen, with an atomic number of 8, has a total of 8 electrons. Now, you see that there are two different coefficients (1 and 2). This tells us that oxygen’s electrons occupy two different energy levels. The three letters tell us that the electrons are spread over three different sublevels. The first energy level (n = 1) has one sublevel, whereas the second energy level (n = 2) has two. The six electrons that occupy the second energy level (2s²2p⁴) represent oxygen’s valence electrons. The nucleus of the atom and the 2 electrons in the first energy level represent the “kernel,” or core, of the atom.

The kernel configuration of the oxygen atom looks just like the electron configuration of the helium atom. We can replace the kernel configuration with the noble gas symbol that it matches, the example: The shorthand electron configuration of Oxygen: [He]2s²2p⁴

3. How to write the electron configuration for elements.

1. Look up the atomic number of the element.

2. Determine the number of electrons for the specific element.

- If the atom is neutral, then the number of electrons is equal to the number of protons.

- If the atom is charged, then algebraically subtract the charge from the atomic number of the element. (Example 1: The atomic number of sodium is 11. An ion of Na⁺ would have a total of 11 – 1 = 10 electrons. Example 2: The atomic number of sulfur is 16. An ion of S^2- would have 16 - (-2) = 18 total electrons)

3. Determine the order in which the sublevels should be filled:

1s 2s2p 3s3p 4s3d4p 5s4d5p 6s4f5d6p 7s5f6d7p

4. Write the configuration, filling in up to 2 electrons in each “s” sublevel, up to 6 electrons in each “p” sublevel, up to 10 electrons in each “d” sublevel, and up to 14 electrons in each “f” sublevel.

5. When you think that you are finished, add up the exponents (superscripts) to see if you have the correct number of electrons.

Ex: Write the full electron configuration for the element aluminum (Al).

Step 1. Look up the atomic number of the element.The periodic table shows us that the atomic number of aluminum is 13.

Step 2. Determine the number of electrons for the specific element.

Because no charge was mentioned, we know that this is a neutral atom. So, the number of electrons = 13.

Step 3. Determine the order in which the sublevels should be filled: 1s 2s2p 3s3p 4s3d4p 5s4d5p 6s4f5d6p 7s5f6d7p.

Step 4. Write the configuration, filling in up to 2 electrons in each “s” sublevel, up to 6 electrons in each “p” sublevel, up to 10 electrons in each “d” sublevel, and up to 14 electrons in each “f” sublevel.We have 1s²2s²2p⁶3s²3p¹, and that brings us up to 13 electrons.

Step 5. When you think that you are finished, add up the exponents (superscripts) to see if you have the correct number of electrons.

Adding the exponents of 1s²2s²2p⁶3s²3p¹ (2 + 2 + 6 + 2 + 1), we get 13 electrons, so our configuration is probably correct.

The full electron configuration for the element aluminum (Al): 1s²2s²2p⁶3s²3p¹

Were you surprised that we only placed 1 electron in the 3p sublevel? Remember that when we say that a “p” sublevel can hold up to 6 electrons, we mean that 6 is the maximum that it can hold. In this case, we only had to place 1 electron in the final “p” sublevel to get up to 13 total electrons.

The shorthand electron configuration of Aluminum: [Ne]3s²3p¹

4. Exceptions to write the electron configuration for elements.

The building up principle reproduces most of the ground state configurations correctly. There are some exceptions, however, and chromium (Z = 24) is the first we encounter. The building-up principle predicts the configuration [Ar]3d⁴4s², though the correct one is found experimentally to be [Ar]3d⁵4s¹. These two configurations are actually very close in total energy because of the closeness in energies of the 3d and 4s orbitals. For that reason, small effects can influence which of the two configurations is actually lower in energy. Copper (Z = 29) is another exception to the building-up principle, which predicts the configuration [Ar]3d⁹4s², although experiment shows the ground-state configuration to be [Ar]3d¹⁰4s¹.

D. EXERCISES

1. Match the following terms to the definitions that follow. Not all answers will be used.

a. proton b. neutron c. electron d. mass number e.atomic number

f. kernel g. negative h. elemental notation i. positive

j. quantum numbers k. valence l. orbital

_____1. A negatively charged particle found in the cloud region of the atom.

_____2. The nucleus and all of the electrons, except the valence electrons.

_____3. The total number of protons and neutrons in an atom.

_____4. A space that can be occupied by up to two electrons.

_____5. This type of ion is formed when an atom loses some electrons.

_____6. Each electron is described by a set of four of these.

_____7. This number is equal to the number of protons in an atom.

_____8. This type of ion is formed when an atom gains additional electrons.

_____9. A positively charged particle found in the nucleus of an atom.

10. Which element is represented by this elemental notation?

11. What is the atomic number of the element?

12. What is the mass number of the element?

13. How many protons does the element have?

14. How many neutrons does the element have?

15. How many electrons does the element have?