Chapter 2.3 - Isotopes, Isobars and Isotones

In the previous section, we saw the Bohr model electronic configuration of atoms. We also saw some solved examples. In this section, we will learn about Isotopes, Isobars and Isotones.

We have seen that the number of protons in an atom is unique. It is the atomic number Z, and it will not change. It is the identity of the element. We have also seen that, in addition to protons, the nucleus contains neutrons also. The number of neutrons may not be the same in all atoms of the same element. Consider an example:

Fig.2.15

• In fig.2.15(a), the atom has 1 proton, 1 electron, and 0 neutron. So it's mass number A = Z + No. Of neutrons = 1 + 0 = 1 
• In fig(b), the atom has 1 proton, 1 electron, and 1 neutron.  So it's mass number A = Z + No. Of neutrons = 1 + 1 = 2
• In fig(c), the atom has 1 proton, 1 electron, and 2 neutrons.  So it's mass number A = Z + No. Of neutrons = 1 + 2 = 3


In all the three cases, the number of protons is the same. So the three atoms belong to the same element. Though they belong to the same element, the mass is different. So we need a method to distinguish between the three. For this, we use the term 'isotopes'. In the above fig.2.15, the three atoms are 'isotopes of the same element'. 

In the fig., the element shown is hydrogen. Because  Z = 1. So we say: The three atoms are 'isotopes of hydrogen'. The three isotopes of hydrogen are:
• Protium Z = 1, A = 1
• Deutirium Z =1, A = 2
• Tritium Z = 1, A = 3

Representation of Isotopes

We have seen that the elements are represented by their symbols. We have also seen that the Z is written on left side bottom, and A on left side top. This same method can be used to represent isotopes also. The isotopes of hydrogen are represented as shown below:

(a) represents Protium, (b) represents Deuterium, and (c) represents Tritium  

In the same way, the isotopes of carbon can be represented as:

(a) represents Carbon-12, (b) represents Carbon-13, and (c) represents Carbon-14

Uses of isotopes
Isotopes find application in many fields. Some examples are:
• Carbon-14 is used to determine the age of fossils and prehistoric objects
• Deuterium is used in atomic reactors

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So we have seen the details about isotopes. It involves the combination of two items: (i) Atomic number Z (same), and (ii) Mass number A (different)
Other combinations are also possible. Consider the example given below:

(a) is Argon. It has Z = 18 and A = 40
(b) is Calcium. It has Z = 20 and A = 40
Note that both have A same. Such elements having same mass number but different atomic numbers are called isobars. The combination here is: (i) Atomic number Z (different), and (ii) Mass number A (same).

Another combination that is possible is, (i) Atomic number (different) and (ii) Number of neutrons (same). An example is given below:

(a) is Nitrogen. It has Z = 7 and A = 15. There fore number of neutrons = 15 -7 = 8
(b) is Carbon-14. It has Z = 6 and A = 14. There fore number of neutrons = 14 - 6 = 8 

Number of neutrons is the same. Such elements having different atomic numbers but same number of neutrons are called isotones.

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We will now see some solved examples
Solved example 2.6
Bohr models of atoms A, B, C and D (symbols are not real) are given below:

(a) Write the atomic number, mass number and electronic configuration of the atoms
(b) Among these, which are isotopes? why?
Solution:
■ (A) has 6 protons in it's nucleus. So the atomic number Z = 6
• It has 6 neutrons in the nucleus. So mass number = No. of protons + No. of neutrons = 6 + 6 = 12
• It has 2 electrons in the K-shell and 4 electrons in the L-shell. So the electronic configuration is 2,4

■ (B) has 7 protons in it's nucleus. So the atomic number Z = 7
• It has 8 neutrons in the nucleus. So mass number = No. of protons + No. of neutrons = 7 + 8 = 15
• It has 2 electrons in the K-shell and 5 electrons in the L-shell. So the electronic configuration is 2,5

■ (C) has 6 protons in it's nucleus. So the atomic number Z = 6
• It has 8 neutrons in the nucleus. So mass number = No. of protons + No. of neutrons = 6 + 8 = 14
• It has 2 electrons in the K-shell and 4 electrons in the L-shell. So the electronic configuration is 2,4

■ (D) has 8 protons in it's nucleus. So the atomic number Z = 8
• It has 8 neutrons in the nucleus. So mass number = No. of protons + No. of neutrons = 6 + 8 = 14
• It has 2 electrons in the K-shell and 6 electrons in the L-shell. So the electronic configuration is 2,6

■ Among the above four atoms, (A) and (C) are isotopes because they both have the same atomic number Z = 6, and different mass numbers. (A) has mass number 12, and (C) has mass number 14. It can be represented as:

Solved example 2.7
Symbols (not real symbols) of some atoms are given below

(a) Find the atomic number and mass number of these elements
(b) Which among these are isotopic pairs
(c) Draw the bohr model of atom Q 
Solution:
a. (P) has atomic number Z = 8 and mass number A = 17
(Q) has atomic number Z = 18 and mass number A = 36
(R) has atomic number Z = 8 and mass number A = 16

b. (P) and (R) are isotopic pairs. because they have the same atomic number Z = 8, and different mass numbers. P has mass number = 17 and Q has mass number = 16

c.The Bohr model of atom Q is shown below:

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In the next chapter we will see 'Chemical bonding'.

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Chapter 2 - Mass of Protons, Neutrons and Electrons

In the previous section, we saw the details about Chemical equations. In this chapter, we will see Details of Atoms.

We have seen elements, compounds, molecules, atoms etc., The objects that we learn about, are becoming smaller and smaller. Compare this with the research of astronomers: They explore more and more by studying higher and higher levels. Like, upper atmosphere, outer space, deep space etc., The objects that they deal with, become larger and larger. Like planets, stars, etc.,

We are going in the opposite direction. The objects that we study, become smaller and smaller. The comparison is shown in the fig.2.1 below:

Fig.2.1

We have seen molecules and atoms. Now we go still deeper. We want to know what is inside the atoms. At the center of the atom, there is the nucleus. Different types of particles are present inside the nucleus. One such particle is the Proton. It is a positively charged particle. Each atom of a particular element will have a particular number of protons. For example,
• an atom of Sodium will have 11 protons in it’s nucleus
• an atom of Nitrogen will have 7 protons in it’s nucleus
The number of protons in the atom of a particular element is a unique value, that will never change.

Even when the nucleus carries positively charged protons, the atom as a whole, is electrically neutral. Why is that so? The answer is that, the positive charge is neutralised by another type of particle called the Electron. This electron is a negatively charged particle. And the number of electrons in an atom will be equal to the number of protons. So the charges get neutralised. The electrons revolve around the nucleus. Just like planets revolve around the sun. The electrons revolve around the nucleus in fixed orbits. These orbits are also called shells. This is shown in the fig.2.2 below:

Fig.2.2

The shells around the nucleus are given fixed numbers. The numbering is done starting from the shell which is closest to the nucleus. So the shell which is closest to the nucleus will be numbered 1. The next shell 2, and so on. Larger the number of a shell, greater is it’s distance from the nucleus. In addition to numbering, the shells are also given names. K, L, M, N etc., So the shell number 1 is called the K-shell, shell number 2 is called the L-shell, shell number 3 is called the M-shell and so on.

The above model was put forward by Danish scientist Neils Bohr, and is called the Bohr model of atom.

Mass of particles
If we take a piece of iron in our hand, we will feel some weight. This is because, the iron piece that we took has ‘mass’. If we take a piece of wood of the same size, we will not feel the same weight. This is because, iron has more mass than wood of the same size. All substances have mass, even if they are very small. Molecules, atoms, protons, electrons.., all have mass.

When scientists studied about the mass of atoms, protons, electrons etc., they noticed an important difference:
Consider the following sum:
• Total mass of all the protons in an atom + Total mass of all the electrons in that atom.
The above sum must be equal to the ‘mass of the atom as a whole’. This is because, the atom consists of protons in the central nucleus, and the electrons revolving around the nucleus.

But it was found that, the above sum was very less than the mass of the atom. This is shown schematically in the fig. 2.3 below:

Fig.2.3

Based on this difference, scientists predicted that, protons and electrons are not the only components of an atom. Some thing else is also present.

In 1932, British scientist James Chadwick discovered the unknown particle. It was named as Neutrons. They are present in the nucleus of the atom. They are neither positively charged nor negatively charged. That is., they are electrically neutral. So we can include neutrons also, in the calculations related to mass.

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In day to day life, we require various units to make various measurements. For example, 
• We use the unit ‘meter’ to measure distances. 
• We use the unit kilogram to measure mass (or weight)
In the same way, we now need an ‘appropriate unit’ to measure very small masses. Because, electrons, protons etc., have very small masses. The unit that we use for this purpose is called the Atomic mass unit. It is abbreviated as u, just as meter is abbreviated as m and kilogram is abbreviated as kg.

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Now we must discuss an important point: 
■ One meter is the distance travelled by light in 1/299,792,458 of a second. So we have a condition: The distance travelled by light during a certain time. Such a condition puts a ‘fix’ on the meter. The advantage of having a ‘fix’ is that, different people will not take different values for ‘one meter’.
■ One gram also have a fix. It is the mass of 1 cm³ of water. From this, the mass corresponding to 1 kg can be easily calculated because, 1 kg = 1000 g
■ In the same manner, we want a fix on ‘u’ also. It is done as follows:
• One u is 1/12 of the mass of a carbon-12 atom
• One carbon-12 atom has a mass of 1.992646547 × 10 ^-27 kg
• 1/12 of that is 1.6605 × 10 ^-27 kg
• So, one u = 1.6605 × 10 ^-27

What is this ‘carbon-12 atom’ ? Why not just say ‘carbon atom’? 
Carbon-12 is a close relative of carbon. ‘12’ is strictly specified so that, there will not be any ambiguity while choosing from among close relatives who are ‘look-alikes’. We will learn about the relation later in this chapter.
Any way, it is not important for our present discussion. All we need to know at present is that 1 u = 1.6605 × 10 ^-27

So we have a 10, raised to the power of -27. let us analyse it further:
1 kg mass is known to us
• 0.1 kg = 10 ^-1 = one tenth of a kg
• 0.01 kg = 10 ^-2 = one hundredth of a kg. A smaller quantity.
• 0.001 kg = 10 ^-3 = It is a very small quantity. It comes into use when we measure the mass of precious metals like gold
• 0.0001 kg = 10 ^-4 . A still smaller quantity.

Notice that when the number of zeros (on the right side of the decimal point) increases, the quantity becomes smaller and smaller. 1.6605 × 10 ^-27 will have 26 zeros on the right side of the decimal point. It is an extremely small quantity. 

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Now we need to express the masses of electrons, protons etc., in terms of u. So that we can just write ‘u’ instead of 1.6605 × 10 ^-27. How do we do that​?

It is an ordinary case of ‘conversion from one unit to another’. Let us see a common example.
Suppose we have Rs. 2500/- with us. How many Euros is that? We can easily calculate it if we know ‘how much is one Euro in Rs.’ At the present rate, One Euro = 74.44 Rs. So Rs. 2500 = 2500/74.44 = 33.58 Euros. In this way we can convert the 'mass of a proton in kg', into 'mass of a proton in u'. The following comparison will help to understand the process better:

So we find that the procedure is to simply divide. 
• If we have Rs 2500/-, it is equivalent to having 33.58 Euros. 
• If we have 1.6605 × 10 ^-27 kg, it is equivalent to having 1.00727 u
In this way we can express the mass of neutron and electron also in terms of u. The steps are shown below:

For easy comparison, let us write the results together:
• Mass of Proton = 1.00727 u
• Mass of Neutron = 1.00866 u
• Mass of Electron = 0.005484 u

Consider the mass of proton. There are 2 zeros after the decimal point. That means, the quantity after the decimal point is small. So, for practical purposes, this portion after the decimal point is discarded. That leaves ‘1’ on the left side of the decimal point. That means, for practical purposes, the mass of one proton is taken as 1u

Next consider the mass of neutron. Here also there are 2 zeros after the decimal point. That means, the quantity after the decimal point is small. So, for practical purposes, this portion after the decimal point is discarded. That leaves ‘1’ on the left side of the decimal point. That means, for practical purposes, the mass of one neutron is taken as 1u


Now consider the mass of electron. Here also there are 2 zeros after the decimal point. That means, the quantity after the decimal point is small. So, for practical purposes, this portion after the decimal point is discarded. That leaves ‘0’ on the left side of the decimal point. That means, for practical purposes, the mass of neutron is taken as 0 u. So the neutron is given 'zero mass' in calculations.

The above calculations tallies with the experimental results. Experimentally, it is proved that most of the mass of an atom is concentrated in the nucleus. That is., total mass of the atom is due mainly to the nucleus. The electrons out side the nucleus does not contribute much to the total mass of the atom. This is shown schematically in the fig.2.4 below. 

Fig.2.4

So it is appropriate to consider electrons to have zero mass.

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In the next section we will see 'Mass number'.

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