October 19th - Atoms, Isotopes, and Mass Spectrometers

Today, the class started with a quick review of the homework. While going over the questions, we came across two new concepts; orbital diagrams and excited/ground states.

Orbital diagrams are diagrams that give us information about the orbitals and the pattern of electrons in an atom. Just like we can use electron configuration notation, we can use orbital diagrams to describe electron configuration. When drawing orbital diagrams, we start by drawing boxes to represent each orbital. Remembering that each orbital holds two electrons, we can draw two electrons in each box. Electrons are represented by arrows in orbital diagrams. For example, the 1s orbital will have one box with two arrows. The second will also have one box. However, the third box will be made of three boxes, each with two arrows. To properly draw a diagram, we must also follow the Aufbau Principle, the Pauli Exclusion Principle, and Hund's Rule. The first principle states that electrons are added one at a time to the lowest energy orbitals until all electrons in the atom are accounted for. The second principle states that each orbital can only hold two electrons. Both electrons must be pointed in different directions, representing their different spins. For example, you can never have a box with two 'up' arrows. Finally, according to Hund's rule, electrons occupy orbitals so that a maximum number of unpaired electrons result. For example, when adding arrows to the three boxes that make up the 2p orbital, we would add one to each box before we start pairing. Here's an example an orbital diagram for the element nitrogen:

The diagram above showed nitrogen in it's ground state. The ground state of an atom is the state where the atom's electrons occupy the lowest energy orbitals available. It is the lowest, most stable state of an atom. In most cases, the diagrams and electron configuration notation will represent an atom in it's ground state. However, you will sometimes encounter something like this:

1s²2s²2p⁶3p

 You may be asking yourself why there is an electron in the 3p orbital, but none in the 3s orbital. This is because this atom is in it's excited state. Basically, the excited state of an atom is a state with more energy. You can find out the atomic number by counting the number of electrons; the number remains the same. However, if you notice that an orbital has been skipped, you will know that it is excited.

Now, onto the main lesson of the day; isotopes and atoms! On the periodic table, you will encounter information such as this:

This tells you the atomic number (top left), the symbol (centre), the ion charge (bottom right), and the mass (top right). To find the number neutrons, you can use this information. Simply apply the formula atomic mass - atomic number = neutron number. However, it is important to note that the atomic mass listed on the table is only the average of all the isotopes of an element. An isotope is a form of an atom with the same number of protons but a different number of neutrons. For magnesium, the isotopes are magnesium-19 to magnesium-40, inclusive. If we add up all the masses and divide it by the number of isotopes, we get the atomic mass! To write the isotope notation for magnesium, we would write the mass of the isotope on top and the atomic number on the bottom, like so:

If we were to look at the atom, we would find that it has twelve protons and twelve neutrons in it's nucleus. However, if were were to look at magnesium-23 and magnesium-25, we would find that they would have one less and one more, respectively.  To simplify this concept, we can use hydrogen. As you can see, the smallest isotope, hydrogen-1, only has one neutron. Deuterium (hydrogen-2) and tritium (hyrdogen-3) each have more neutrons:

The neutrons act as spacers to prevent protons from repelling. This is why the positively charged nucleus doesn't repel itself. 

Going back to magnesium, we can use a device called a mass spectrometer to find out the abundance and mass of all the isotopes of an element. A mass spectrometer uses a charged field to deflect a beam of charged particles (different isotopes). The heaviest particles will bend the least, and the lightest will bend the most. After deflection, we can measure where the particle landed on a screen and in what abundance. With that information, we can find out the different isotopes and their abundance! Here's a diagram of a mass spectrometer: 

With the help of a mass spectrometer, we now have information regarding the abundance of certain isotopes. This graph represents our results:

As you can see, magnesium-24 is the most abundance. However, you may notice that only two of the possible twenty other isotopes are listed. This is because the others are found in such small numbers in a sample that their relative abundance is only a fraction of a percent. This is why the percentage only adds up to 99 on the graph; the remaining 1 is made of the 18 other isotopes. It is also important to note that the same isotopes will be found in the same relative abundance throughout the universe.

We can add up the abundances to find the average atomic mass:

   0.78 x 24.00 amu

+ 0.10 x 25.00 amu

+ 0.11 x 26.00 amu

 24.14 amu

When we add it up, we get 24.14. When we round to 2 significant digits, we get 24 amu. Looking back, we know that the atomic mass of magnesium is 24.305. Using abundances and isotope numbers, we have just calculated average atomic mass!

Note: amu represents 'atomic mass units'. Also note that isotopes with a percentage of less than 1% were not taken into account

Posted by Michael.