In this chapter, we will understand **what is mass number** and how to find it with the help of solved examples.

You have studied that an atom of an element consists of electrons, protons, and neutrons. The nucleus of an atom consists of protons and neutrons. Since the mass of the electron is negligible, therefore, the entire mass of any atom is mainly due to the presence of protons and neutrons in its nucleus. Thus, we can define the mass number as:

The sum of the number of protons and neutrons present in its nucleus is called **mass number** of an atom of an element. Protons and neutrons are collectively called **nucleons**. Mass number is represented by A. Thus, for an atom,

**Mass number (A)** = **number of protons (p) + number of neutrons(n)**

**A = p + n** = **number of nucleons**

As the atomic number of an element (Z) is equal to the number of protons (p) present in the nucleus of its atom, therefore

Mass number (A)** = **Atomic number + number of neutrons present in the nucleus

**A = Z + n (Since Z = p)**

**Number of neutrons (n)** = A – Z

In this way, if you know the atomic number and mass number of an element, you can calculate the number of electrons, protons, and neutrons in the atom of an element.

**Note** that the mass number of an atom is a whole number. You can obtain the mass number by rounding off the experimental value of atomic mass (or atomic weight) to the nearest whole number.

For example, the atomic mass of chlorine and calcium obtained by experiment is 35.453 and 40.078 amu, respectively. Thus, their mass numbers are 35 for chlorine and 40 for calcium.

## Representation of Mass Number and Atomic Number of an Element

The mass number and atomic number of an element are generally represented together in a standard notation called nuclear notation or isotope notation. This is how it is written:

Here’s a breakdown:

**Element Symbol (X)**: This is the chemical symbol of the element, such as C for carbon, O for oxygen, or H for hydrogen.

**Mass Number (A)**: This is written as a superscript to the upper left of the element symbol. It represents the total number of protons and neutrons in the nucleus.

**Atomic Number (Z)**: This is written as a subscript to the lower left of the element symbol. It represents the number of protons present in the nucleus and defines the element.

## What is Nuclide?

Each different variety of an atom, as determined by the composition of its nucleus (i.e., the number of protons and neutrons), is called a **nuclide**. A nuclide is characterized by its atomic number, mass number, and its energy state.

For example, carbon-12 (6 protons, 6 neutrons) and carbon-14 (6 protons, 8 neutrons) are both different nuclides of carbon.

## Solved Examples

Calculate the number of neutrons and protons present in the following nuclides.**Example 1:**

^{13}_{6}C^{16}_{8}O^{24}_{12}Mg^{56}_{26}Fe^{88}_{38}Sr

`Solution: `

(1) ^{13}_{6}C : Z = 6 and A = 13

Number of protons (p) = Atomic number (Z) = 6 (Ans.)

Number of neutrons (n) = A – Z = 13 – 6 = 7 (Ans.)

(2) ^{16}_{8}O : Z = 8 and A = 16

Number of protons (p) = Z = 8 (Ans.)

Number of neutrons (n) = A – Z = 16 – 8 = 8 (Ans.)

(3) ^{24}_{12}Mg : Z = 12 and A = 24

Number of protons (p) = Z = 12 (Ans)

Number of neutrons (n) = A – Z = 24 – 12 = 12 (Ans)

(4) ^{56}_{26}Fe : Z = 26 and A = 56

Number of protons (p) = Z = 26 (Ans)

Number of neutrons (n) = A – Z = 56 – 26 = 30 (Ans)

(5) ^{88}_{38}Sr : Try yourself.

** Example 2:** Write the atomic symbol for the atom with given atomic number (Z) and mass number (A).

- Z = 17, A = 35
- Z = 92, A = 233
- Z = 4, A = 9

`Solution:`

(1) ^{35}_{17}Cl

(2) ^{233}_{92}U

(3) ^{9}_{4}Be

** Example 3:** An element with mass number 81 contains 31.7% more neutrons than protons. Write its atomic symbol.

** Solution:** Given, A = 81. So, p + n = 81.

Number of neutrons (n) = p + p * (31.7 / 100) = (100p + 31.7p)/100 = 131.7p / 100

Since 81 – p = 131.7p / 100

131.7p / 100 + p = 81

231.7p / 100 = 81

p = 81 *100 / 231.7 = 34.96

Since p has to be whole number, therefore, number of protons (p) = 35.

Number of neutrons (n) = A – p = 81 – 35 = 46.

The nuclide symbol is ^{81}_{35}Br.

** Example 4:** Calculate the number of electrons, protons, and neutrons present in uranium with the given atomic number 92 and atomic weight 238.029.

`Solution:`

Given, atomic number of uranium = 92

Therefore, number of electrons = 92 = number of protons

Number of neutron (n) = A – Z

Mass number (A) is obtained by rounding off the atomic weight =238.029 = 238.

Therefore, n = A – Z = 238 – 92 = 146.

Thus, uranium atom has 92 electrons, 92 protons, and 146 neutrons.

** Example 5: **An ion with mass number 37 contains one unit of negative charge and 11.1% more neutrons than electrons. What is the symbol of this ion?

** Solution: **Given, mass number A = p + n = 37.

Since the ion has one unit of negative charge, it has one more electron than protons.

If the number of protons is p, then number of electrons e = p + 1.

Let the number of electrons be e.

Then, number of neutrons (n) = e + 11.1e / 100

Therefore, n = (p + 1) + 11.1 (p + 1)/100

n = (10p + 10)/9

But, n = 37 – p

37 – p = (10p + 10)/9

37 * 9 – 9p = 10p + 10

p = 17

Since number of protons = 17 = Atomic number

Atomic number Z = 17

Mass number A = 37

The ion is has one unit of negative charge, so it is Cl with a charge of −1.

The symbol for ion is ^{37}_{17}Cl^{–}.

** Example 6:** An ion with mass number 56 possesses three unit of positive charge. If the ion contains 30.4% more neutrons than electrons, then find the symbol of this ion.

** Solution: **Given, A = 56 = p + n.

Since the ion has three units of positive charge, it has three fewer electrons than protons. Thus, if the number of protons is p, then the number of electrons is p – 3.

Let the number of electrons be e.

Then, the number of neutrons (n) = e + 30.4e / 100 = 130.4e/100

n = 130.4(p – 3)/100

Since, n = 56 – p

Therefore, 56 – p = 130.4(p – 3)/100

5600 – 100p = 130.4p – 391.2

130.4p + 100p = 5600 + 391.20

230.4p = 5991.2

p = 26.

Thus, atomic number (Z) = number of protons (p) = 26.

Mass number (A) = 56.

The ion is has three unit of positive charge, so it is Fe with a charge of +3.

The symbol for ion is ^{56}_{26}Fe^{+3}.

** Example 7: ** Find the number of protons, electrons, and neutrons present in 0.18 grams of

^{30}

_{15}P.

** Solution: **Number of protons in one atom of P = Number of electrons in one atom of P = 15 (given).

Mass number (A) = 30 (given)

Number of neutrons in one atom of P = A – Z = 30 – 15 = 15.

Mass of the sample = 0.18 grams (given)

Molar mass of phosphorus = 30 grams per mole.

Number of moles of ^{30}_{15}p in 0.18 grams is given by

Number of moles = Mass of sample / Molar mass = 0.18g / 30 gmol^{-1} = 0.006 mol

Number of phosphorus atoms in 0.006 moles = 0.006 mol * 6.022×10^{23} atoms/mol

Number of atoms=3.6132×10^{21} atoms

Since each phosphorus atom has 15 protons, so the total number of protons is given by:

Number of protons = 15 × 3.6132 × 10^{21} = 5.4198 × 10^{22} protons (Ans)

Since the phosphorus atom is neutral, it has 15 electrons as well. The total number of electrons is given by:

Number of electrons = 15 × 3.6132 × 10^{21} = 5.4198 × 10^{22} electrons (Ans)

Similarly, each phosphorus atom has 15 neutrons. The total number of neutrons is given by:

Number of neutrons = 15 × 3.6132 × 10^{21} = 5.4198 × 10^{22} neutrons (Ans)

## Difference between Atomic number and Mass number

The main difference between mass number and atomic number are as follows:

Atomic Number (Z):

- The atomic number is the number of protons present inside the nucleus of an atom.
- It defines the identity of the element. For example, all atoms with 6 protons are carbon atoms.
- The atomic number also determines the chemical properties of the element because it defines the number of electrons in a neutral atom.
- Example: In carbon (C), the atomic number is 6 because it has 6 protons.

Mass Number (A):

- The mass number is the total number of protons and neutrons present inside the nucleus of an atom.
- It represents the mass of the atom.
- Mass number = Number of protons + Number of neutrons.
- Example: A carbon atom with 6 protons and 6 neutrons will have a mass number of 12.