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# Isotopes

## Isotopes

### What is an isotope?

The chemical properties of an element depend on the number of protons and electrons inside the atom. So if a neutron or two is added or removed from the nucleus, then the chemical properties will not change. This means that such an atom would remain in the same place in the Periodic Table. For example, no matter how many neutrons we add or subtract from a nucleus with 6 protons, that element will always be called carbon and have the element symbol C (see the Table of Elements). Atoms which have the same number of protons, but a different number of neutrons, are called isotopes.

Definition 1: Isotope

The isotope of a particular element is made up of atoms which have the same number of protons as the atoms in the original element, but a different number of neutrons.

The different isotopes of an element have the same atomic number ZZ but different mass numbers AA because they have a different number of neutrons NN. The chemical properties of the different isotopes of an element are the same, but they might vary in how stable their nucleus is. Note that we can also write elements as X-A where the X is the element symbol and the A is the atomic mass of that element. For example, C-12 has an atomic mass of 12 and Cl-35 has an atomic mass of 35 u, while Cl-37 has an atomic mass of 37 u.

#### Note: Interesting Fact :

In Greek, “same place” reads as ισoςισoςτoπoςτoπoς

(isos topos). This is why atoms which have the same number of protons, but different numbers of neutrons, are called isotopes. They are in the same place on the Periodic Table!

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

#### Exercise 1: Isotopes

For the element 92234U92234U (uranium), use standard notation to describe:

1. the isotope with 2 fewer neutrons
2. the isotope with 4 more neutrons
##### Solution
1. Step 1. 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.

2. Step 2. Rewrite the notation for the isotopes :

Therefore, any isotope of uranium will have the symbol:

U U
(1)

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

92 U 92 U
(2)

Now, if the isotope we want has 2 fewer neutrons than 92234U92234U, then we take the original mass number and subtract 2, which gives:

92 232 U 92 232 U
(3)

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

92 238 U 92 238 U
(4)

#### Exercise 2: Isotopes

Which of the following are isotopes of 2040 Ca 2040 Ca ?

• 19 40 K 19 40 K
• 20 42 Ca 20 42 Ca
• 18 40 Ar 18 40 Ar
##### Solution
1. Step 1. Go over the definition of isotope: :

We know that isotopes have the same atomic number but different mass numbers.

2. Step 2. 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 20422042Ca. What is different is that there are 2 more neutrons than in the original element.

#### Exercise 3: Isotopes

For the sulphur isotope 16331633S, give the number of...

1. protons
2. nucleons
3. electrons
4. neutrons
##### Solution
1. Step 1. Determine the number of protons by looking at the atomic number, Z. :

Z = 16, therefore the number of protons is 16 (answer to (a)).

2. Step 2. 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)).

3. Step 3. 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)).

4. Step 4. Calculate the number of neutrons :
N = A - Z = 33 - 16 = 17 N = A - Z = 33 - 16 = 17
(5)

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

#### Isotopes

1. 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
2. For the sulphur isotopes, 16321632S and 16341634S, give the number of...
1. protons
2. nucleons
3. electrons
4. neutrons
3. Which of the following are isotopes of 17351735Cl?
1. 35173517Cl
2. 17351735Cl
3. 17371737Cl
4. Which of the following are isotopes of U-235? (X represents an element symbol)
1. 9223892238X
2. 9023890238X
3. 9223592235X

### 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.

Definition 2: Relative atomic mass

Relative atomic mass is the average mass of one atom of all the naturally occurring isotopes of a particular chemical element, expressed in atomic mass units.

#### Note: 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.

#### Exercise 4: The relative atomic mass of an isotopic element

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.

##### Solution
1. Step 1. Calculate the mass contribution of chlorine-35 to the average relative atomic mass :

Contribution of Cl-35 = (75/100 x 35) = 26,25 u

2. Step 2. Calculate the contribution of chlorine-37 to the average relative atomic mass :

Contribution of Cl-37 = (25/100 x 37) = 9,25 u

3. Step 3. 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.

#### Isotopes

1. Complete the table below:
 Isotope Z A Protons Neutrons Electrons Carbon-12 Carbon-14 Chlorine-35 Chlorine-37
2. If a sample contains 90% carbon-12 and 10% carbon-14, calculate the relative atomic mass of an atom in that sample.

3. If a sample contains 22.5% Cl-37 and 77.5% Cl-35, calculate the relative atomic mass of an atom in that sample.

#### Group Discussion : The changing nature of scientific knowledge

Scientific knowledge is not static: it changes and evolves over time as scientists build on the ideas of others to come up with revised (and often improved) theories and ideas. In this chapter for example, we saw how peoples' understanding of atomic structure changed as more information was gathered about the atom. There are many more examples like this one in the field of science. For example, think about our knowledge of the solar system and the origin of the universe, or about the particle and wave nature of light.

Often, these changes in scientific thinking can be very controversial because they disturb what people have come to know and accept. It is important that we realise that what we know now about science may also change. An important part of being a scientist is to be a critical thinker. This means that you need to question information that you are given and decide whether it is accurate and whether it can be accepted as true. At the same time, you need to learn to be open to new ideas and not to become stuck in what you believe is right... there might just be something new waiting around the corner that you have not thought about!

In groups of 4-5, discuss the following questions:

• Think about some other examples where scientific knowledge has changed because of new ideas and discoveries:
• What were these new ideas?
• Were they controversial? If so, why?
• What role (if any) did technology play in developing these new ideas?
• How have these ideas affected the way we understand the world?
• Many people come up with their own ideas about how the world works. The same is true in science. So how do we, and other scientists, know what to believe and what not to? How do we know when new ideas are 'good' science or 'bad' science? In your groups, discuss some of the things that would need to be done to check whether a new idea or theory was worth listening to, or whether it was not.
• Present your ideas to the rest of the class.

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