# Mass Number of an Atom Chemistry Tutorial

## Key Concepts

• Mass number of an atom has the symbol A
• The mass number, A, of an element is NOT given in the Periodic Table of the Elements.
• Mass number, A, is the total number of protons and neutrons in the nucleus of an atom.

mass number = number of protons + number of neutrons

A = number of protons + number of neutrons

• The number of protons in the nucleus of an atom is given by the element's atomic number, Z
• Mass number = atomic number + number of neutrons

A = Z + number of neutrons

• The symbol of an element with the symbol X and with mass number A and atomic number Z can be given as1:

 AZ X

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## Mass Number and Number of Neutrons in the Nucleus of an Atom

The nucleus of an atom is composed of two different types of particles, or nucleons.
These nucleons (particles in the nucleus) are:

• protons which have a positive charge (+1)
• neutrons which are electrically neutral, that is, they are uncharged particles

The nucleons (protons and neutrons) have a much greater mass than electrons that surround the nucleus as shown in the table below:

sub-atomic particle mass / kg protons 1.673 × 10-27 neutrons 1.675 × 10-27 electrons 9.109 × 10-31

The mass of a nucleon (a proton or a neutron) is about 1,800 times greater than the mass of an electron.
For this reason, we can confidently assert that most of the mass of an atom is found in the mass of the nucleus, and therefore most of the mass of an atom is the result of the protons and neutrons making up the nucleus of the atom.
This led to the definition of a "mass number" as the number of nucleons (sub-atomic particles found in the nucleus of an atom).

mass number = total number of nucleons

Mass number has been given the symbol A so

A = mass number = total number of nucleons

If an atom of an element is known to have 32 nucleons, then its mass number is 32 or A = 32.
If an atom has a mass number of 79 (A = 79), then the nucleus of this atom contains 79 nucleons.

We also know that the term nucleons refers to both the protons and the neutrons in the nucleus of an atom. So,

mass number = number of protons + number of neutrons

and the number of protons in the nucleus of an atom is equal to the element's atomic number, Z, so

mass number = atomic number + number of neutrons

A = Z + number of neutrons

So, if we know the mass number of an atom of an element is 32 (A = 32) and the atomic number of the element is 16 (Z = 16), then we can calculate the number of neutrons in an atom of this element:

A = Z + number of neutrons

32 = 16 + number of neutrons

32 - 16 = number of neutrons

16 = number of neutrons

If we know the atomic number of an element is 11 (Z = 11) and the number of neutrons in the nucleus of an atom of this element is 12, then we can calculate the mass number (A) of an atom of this element:

A = Z + number of neutrons

A = 11 + 12

A = 23

Chemists have a shortcut for conveying all this information in one symbol.
For an atom of element X with atomic number Z and mass number A, the symbol is

 AZ X

For example, the element sodium has been given the chemical symbol Na (see the Periodic Table)
The atomic number for sodium is 11 (Z = 11) (see the Periodic Table)
Given an atom of sodium with mass number 23 (A = 23)
The symbol for this atom of sodium will be:

 2311 Na

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## Worked Example 1: Mass Number of an Atom

Question : An atom of phosphorus has 16 neutrons in its nucleus.
Determine the mass number for this phosphorus atom.

Solution:

(Based on the StoPGoPS approach to problem solving.)

1. What is the question asking you to do?

Calculate mass number
A = ?

2. What data (information) have you been given in the question?

Extract the data from the question:

element name: phosphorus
number of neutrons in nucleus = 16
3. What is the relationship between what you know and what you need to find out?
A = Z + number of neutrons
where Z = atomic number of phosphorus

Use the Periodic Table of the Elements to find the atomic number (Z) of phosphorus (P):
Z = 15

4. Substitute the values into the equation and solve for mass number of the atom (A)
A = Z + number of neutrons
A = 15 + 16 = 31
(a) Mass number must be a whole number because it is counting the number of nucleons.
31 is a whole number so our answer is plausible.

(b) Work backwards: use your value of mass number and number of neutrons to determine the atomic number (Z)
A = Z + number of neutrons
31 = Z + 16
31 - 16 = Z
15 = Z
Look up atomic number 15 (Z = 15) in Periodic Table and make sure that it refers to an atom of phosphorus.
Since Z = 15 is phosphorus, we are reasonably confident that our answer is plausible.

6. State your solution to the problem "mass number of the atom":

A = 31

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## Worked Example 2: Number of Neutrons in an Atom

Question : The mass number of an atom of strontium is 88.
Determine the number of neutrons in the nucleus of this strontium atom.

Solution:

(Based on the StoPGoPS approach to problem solving.)

1. What is the question asking you to do?

Calculate the number of neutrons
number of neutrons = ?

2. What data (information) have you been given in the question?

Extract the data from the question:

name of element: strontium
Mass number = A = 88
3. What is the relationship between what you know and what you need to find out?
A = Z + number of neutrons
where Z = atomic number of strontium

Use the Periodic Table to determine the atomic number of strontium (Sr):
Z = 38

4. Substitute the values into the equation and solve for number of neutrons:
A = Z + number of neutrons
88 = 38 + number of neutrons
88 - 38 = number of neutrons
50 = number of neutrons
(a) Number of neutrons must be a whole number.
50 is a whole number so our answer is plausible.

(b) Work backwards: use your value of number of neutrons and mass number to determine the atomic number (Z)
A = Z + number of neutrons
88 = Z + 50
88 - 50 = Z
38 = Z
Look up atomic number 38 (Z = 38) in Periodic Table and make sure that it refers to an atom of strontium.
Since Z = 38 is strontium, we are reasonably confident that our answer is plausible.

6. State your solution to the problem "number of neutrons in nucleus":

number of neutrons = 50

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## Worked Example 3: Using Symbol of an Element to Find Number of Neutrons

Question : The symbol of an atom of uranium is shown below:
 23892 U

Determine the number of neutrons in the nucleus of one of these uranium atoms.

Solution:

(Based on the StoPGoPS approach to problem solving.)

1. What is the question asking you to do?

Calculate the number of neutrons
number of neutrons = ?

2. What data (information) have you been given in the question?

Extract the data from the question:

Symbol of the element:
 23892 U

mass number = A = 238
atomic number = Z = 92
3. What is the relationship between what you know and what you need to find out?
A = Z + number of neutrons
where Z = atomic number of
and A = mass number of
4. Substitute the values into the equation and solve for number of neutrons:
A = Z + number of neutrons
238 = 92 + number of neutrons
238 - 92 = number of neutrons
146 = number of neutrons
(a) Number of neutrons must be a whole number.
146 is a whole number so our answer is plausible.

(b) Work backwards: use your value of number of neutrons and atomic number (Z) to determine the mass number (A)
A = Z + number of neutrons
A = 92 + 146 = 238
Since this value for the mass number is the same as that given in the question we are reasonably confident that our answer is plausible.

6. State your solution to the problem "number of neutrons in nucleus":

number of neutrons = 146

1. You may also see the symbol of element X given as ZXA