3.2 Isotopes

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This simulation allows you to see how isotopes and relative atomic mass are inter related.

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Isotopes

Complete the table below:

Isotope Z A Protons Neutrons Electrons

Carbon-12

Carbon-14

Chlorine-35

Chlorine-37
If a sample contains 90% carbon-12 and 10% carbon-14, calculate the relative atomic mass of an atom in that sample.
If a sample contains 22,5% Cl-37 and 77,5% Cl-35, calculate the relative atomic mass of an atom in that sample.

Standard notation shows the chemical symbol, the atomic mass number and the atomic number of an element as follows:

A nuclide is a distinct kind of atom or nucleus characterized by the number of protons and neutrons in the atom. To be absolutely correct, when we represent atoms like we do here, then we should call them nuclides.

For example, the iron nucleus which has 26 protons and 30 neutrons, is denoted as:

_{26}^{56} Fe

where the atomic number is $Z = 26$ and the mass number $A = 56$ . The number of neutrons is simply the difference $N = A - Z$ .

The following worked examples will help you to understand the concept of an isotope better.

For the element $_{92}^{234} U$ (uranium), use standard notation to describe:

the isotope with 2 fewer neutrons
the isotope with 4 more neutrons

Go over the definition of isotope
We know that isotopes of any element have the same number of protons (same atomic number)in each atom, which means that they have the same chemical symbol. However, they have a different number of neutrons, and therefore a different mass number.
Rewrite the notation for the isotopes
Therefore, any isotope of uranium will have the symbol:

$U$

Also, since the number of protons in uranium isotopes is always the same, we can write down the atomic number:

$_{92} U$

Now, if the isotope we want has 2 fewer neutrons than $_{92}^{234} U$ , then we take the original mass number and subtract 2, which gives:

$_{92}^{232} U$

Following the steps above, we can write the isotope with 4 more neutrons as:

$_{92}^{238} U$

Which of the following are isotopes of $_{20}^{40} Ca$ ?

$_{19}^{40} K$
$_{20}^{42} Ca$
$_{18}^{40} Ar$

Go over the definition of isotope:
We know that isotopes have the same atomic number but different mass numbers.
Determine which of the elements listed fits the definition of an isotope.
You need to look for the element that has the same atomic number but a different atomic mass number. The only element is $_{20}^{42} Ca$ . What is different is that there are 2 more neutrons than in the original element.

For the sulphur isotope $_{16}^{33} S$ , give the number of...

protons
nucleons
electrons
neutrons

Determine the number of protons by looking at the atomic number, Z.
$Z = 16$ , therefore the number of protons is 16 (answer to (a)).
Determine the number of nucleons by looking at the atomic mass number, A.
$A = 33$ , therefore the number of nucleons is 33 (answer to (b)).
Determine the number of electrons
The atom is neutral, and therefore the number of electrons is the same as the number of protons. The number of electrons is 16 (answer to (c)).
Calculate the number of neutrons
$\begin{matrix} N = A - Z = 33 - 16 = 17 \end{matrix}$

The number of neutrons is 17 (answer to (d)).

Isotopes

Atom A has 5 protons and 5 neutrons, and atom B has 6 protons and 5 neutrons. These atoms are...
1. allotropes
2. isotopes
3. isomers
4. atoms of different elements
For the sulphur isotopes, 16 32 S and 16 34 S , give the number of...
1. protons
2. nucleons
3. electrons
4. neutrons
Which of the following are isotopes of 17 35 Cl ?
1. $_{35}^{17} Cl$
2. $_{17}^{35} Cl$
3. $_{17}^{37} Cl$
Which of the following are isotopes of U- 235 ? (X represents an element symbol)
1. $_{92}^{238} X$
2. $_{90}^{238} X$
3. $_{92}^{235} X$

Relative atomic mass

It is important to realise that the atomic mass of isotopes of the same element will be different because they have a different number of nucleons. Chlorine, for example, has two common isotopes which are chlorine-35 and chlorine-37. Chlorine-35 has an atomic mass of 35 u, while chlorine-37 has an atomic mass of 37 u. In the world around us, both of these isotopes occur naturally. It doesn't make sense to say that the element chlorine has an atomic mass of 35 u, or that it has an atomic mass of 37 u. Neither of these are absolutely true since the mass varies depending on the form in which the element occurs. We need to look at how much more common one is than the other in order to calculate the relative atomic mass for the element chlorine. This is the number that you find on the Periodic Table.

Interesting fact

The relative atomic mass of some elements depends on where on Earth the element is found. This is because the isotopes can be found in varying ratios depending on certain factors such as geological composition, etc. The International Union of Pure and Applied Chemistry (IUPAC) has decided to give the relative atomic mass of some elements as a range to better represent the varying isotope ratios on the Earth. For the calculations that you will do at high school, it is enough to simply use one number without worrying about these ranges.

The element chlorine has two isotopes, chlorine-35 and chlorine-37. The abundance of these isotopes when they occur naturally is 75% chlorine-35 and 25% chlorine-37. Calculate the average relative atomic mass for chlorine.

Calculate the mass contribution of chlorine-35 to the average relative atomic mass
Contribution of $Cl- 35 = (\frac{75}{100} \times 35) = 26, 25 u$
Calculate the contribution of chlorine-37 to the average relative atomic mass
Contribution of $Cl- 37 = (\frac{25}{100} \times 37) = 9, 25 u$
Add the two values to arrive at the average relative atomic mass of chlorine
$Relative atomic mass of chlorine = 26, 25 u + 9, 25 u = 35, 5 u$

If you look on the periodic table, the average relative atomic mass for chlorine is $35, 5 u$ . You will notice that for many elements, the relative atomic mass that is shown is not a whole number. You should now understand that this number is the average relative atomic mass for those elements that have naturally occurring isotopes.

This simulation allows you to see how isotopes and relative atomic mass are inter related.

run demo

Isotopes

Complete the table below:

Isotope Z A Protons Neutrons Electrons

Carbon-12

Carbon-14

Chlorine-35

Chlorine-37
If a sample contains 90% carbon-12 and 10% carbon-14, calculate the relative atomic mass of an atom in that sample.
If a sample contains 22,5% Cl-37 and 77,5% Cl-35, calculate the relative atomic mass of an atom in that sample.

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Source: OpenStax, Siyavula textbooks: grade 10 physical science [caps]. OpenStax CNX. Sep 30, 2011 Download for free at http://cnx.org/content/col11305/1.7

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Isotope	Z	A	Protons	Neutrons	Electrons
Carbon-12
Carbon-14
Chlorine-35
Chlorine-37