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Finding the Number of Electrons in an Atom Using Atomic Number (Z)
A proton is a positively charged sub-atomic particle that is found in the nucleus of an atom.
Each proton carries a charge of +1.
An electron is a negatively charged sub-atomic particle that is found in the volume of space surrounding the nucleus of an atom.
Each electron carries a charge of -1.
An atom of an element carries no overall electric charge, that is, the overall charge on an atom is 0.
Since an atom is made up of positively charged protons in the nucleus and negatively charged electrons surrounding the nucleus this means that the number of protons and the number of electrons must be the same.
For an atom of an element:
number of protons in nucleus = number of electrons surrounding nucleus
We know that the atomic number (Z) of an element tells us how many protons are in the nucleus of an atom of that element, so, the number of electrons in an atom of this element must also be equal to the atomic number (Z) of the element:
number of electrons in atom = atomic number = Z
Consider an atom of the element lithium.
Using the Periodic Table we find that lithium has the symbol Li and an atomic number (Z) of 3.
This tells us that there will be 3 protons in the nucleus of an atom of lithium.
Since each proton carries a charge of +1, we could represent the number of charged protons in the nucleus in a diagram like the one below:
| 3 positively charged protons in Li nucleus: |
+ |
+ |
+ |
|---|
Now, each electron surrounding the nucleus of an atom of lithium carries a charge of -1, so we will need 3 electrons to "cancel out" the charge of the 3 protons in the nucleus:
| 3 positively charged protons in Li nucleus: |
+ |
+ |
+ |
|---|
| 3 negatively charged electrons surrounding the Li nucleus: |
- |
- |
- |
|---|
And so the overall, or net, charge on an atom of lithium is zero because +1 + -1 = 0:
| 3 positively charged protons in Li nucleus: |
+ |
+ |
+ |
|---|
| 3 negatively charged electrons surrounding the Li nucleus: |
- |
- |
- |
|---|
| Net Charge: |
0 |
0 |
0 |
|---|
Number of Electrons in Atoms of the First Twenty Elements in the Periodic Table
Below is an extract from the Periodic Table showing the atomic numbers (Z), the symbols and names for the first twenty elements:
| |
Group
1 |
Group
2 |
Groups
3 - 12 |
Group
13 |
Group
14 |
Group
15 |
Group
16 |
Group
17 |
Group
18 |
| Period 1 |
1
H
hydrogen
|
|
2
He
helium
|
| Period 2 |
3
Li
lithium
|
4
Be
beryllium
|
|
5
B
boron
|
6
C
carbon
|
7
N
nitrogen
|
8
O
oxygen
|
9
F
fluorine
|
10
Ne
neon
|
| Period 3 |
11
Na
sodium
|
12
Mg
magnesium
|
|
13
Al
aluminium
|
14
Si
silicon
|
15
P
phosphorus
|
16
S
sulfur
|
17
Cl
chlorine
|
18
Ar
argon
|
| Period 4 |
19
K
potassium
|
20
Ca
calcium
|
|
Since the atomic number (Z) of an element tells us hown many protons are in the nucleus of the atom of that element, and we know that for an atom of the element the number of electrons is equal to the number of protons, we can draw up a table to show the name, symbol, atomic number (Z), number of protons in the nucleus, and, number of electrons surrounding the nucleus of the atom as shown below:
| Name of Element |
Symbol of Element |
Atomic Number of Element (Z) |
Number of Protons in Nucleus of an Atom (= Z) |
Number of Electrons Surrounding the Nucleus of an Atom (= Z) |
|---|
| hydrogen |
H |
1 |
1 |
1 |
| helium |
He |
2 |
2 |
2 |
| lithium |
Li |
3 |
3 |
3 |
| beryllium |
Be |
4 |
4 |
4 |
| boron |
B |
5 |
5 |
5 |
| carbon |
C |
6 |
6 |
6 |
| nitrogen |
N |
7 |
7 |
7 |
| oxygen |
O |
8 |
8 |
8 |
| fluorine |
F |
9 |
9 |
9 |
| neon |
Ne |
10 |
10 |
10 |
| sodium |
Na |
11 |
11 |
11 |
| magnesium |
Mg |
12 |
12 |
12 |
| aluminium |
Al |
13 |
13 |
13 |
| silicon |
Si |
14 |
14 |
14 |
| phosphorus |
P |
15 |
15 |
15 |
| sulfur |
S |
16 |
16 |
16 |
| chlorine |
Cl |
17 |
17 |
17 |
| argon |
Ar |
18 |
18 |
18 |
| potassium |
K |
19 |
19 |
19 |
| calcium |
Ca |
20 |
20 |
20 |
Worked Examples of Finding the Number of Electrons in an Atom
Question 1:
An atom of an element has a nucleus containing 72 protons.
How many electrons surround the nucleus of an atom of this element?
Solution:
(Based on the StoPGoPS approach to problem solving.)
- What is the question asking you to do?
Find the number of electrons surrounding the nucleus of the atom
- What data (information) have you been given in the question?
Extract the data from the question:
number of protons = 72
- What is the relationship between what you know and what you need to find out?
At atom has no overall charge.
number of positive charges = number of negative charges
number of protons = number of electrons
- Determine the number of electrons surrounding the nucleus of the atom
number of protons = number of electrons
72 = number of electrons
- Is your answer plausible?
(a) The number of protons, and therefore the number of electrons, must be a whole number, an integer. 72 is a whole number, so our answer is plausible.
(b) For an atom to have no overall charge (0 net charge):
total positive charge + total negative charge = 0
total positive charge = 72 × +1 = +72
total negative charge = 72 × -1 = -72
+72 + -72 = 0
so our answer is plausible
- State your solution to the problem "number of electrons surround the nucleus of the atom":
Number of electrons = 72
Question 2:
Determine the number of electrons in an atom of chlorine.
Solution:
(Based on the StoPGoPS approach to problem solving.)
- What is the question asking you to do?
Find the number of electrons in an atom of chlorine
- What data (information) have you been given in the question?
Extract the data from the question:
Name of element: chlorine
- What is the relationship between what you know and what you need to find out?
number of electrons in atom = number of protons in the nucleus of the atom = atomic number (Z)
Use the Periodic Table to find the atomic number (Z) of chlorine:
Z(chlorine) = 17
- Determine the number of electrons in an atom of chlorine
number of electrons = number of protons = atomic number (Z) = 17
- Is your answer plausible?
(a) The number of protons, and therefore the number of electrons, must be a whole number, an integer. 17 is a whole number, so our answer is plausible.
(b) For an atom to have no overall charge (0 net charge):
total positive charge + total negative charge = 0
total positive charge = 17 × +1 = +17
total negative charge = 17 × -1 = -17
+17 + -17 = 0
so our answer is plausible
- State your solution to the problem "number of electrons in the atom":
Number of electrons = 17
Question 3:
An element has the symbol Fe. Calculate the number of electrons surrounding the nucleus of an atom of this element.
Solution:
(Based on the StoPGoPS approach to problem solving.)
- What is the question asking you to do?
Calculate the number of electrons in an atom of element with symbol Fe
- What data (information) have you been given in the question?
Extract the data from the question:
Symbol of the element: Fe
- What is the relationship between what you know and what you need to find out?
number of electrons = number of protons = atomic number of element = Z
Use the Periodic Table to find the symbol Fe and hence its atomic number (Z):
Z(Fe) = 26
- Calculate the number of protons in an atom of Fe
number of electrons = number of protons = atomic number = 26
- Is your answer plausible?
(a) The number of protons, and therefore the number of electrons, must be a whole number, an integer. 26 is a whole number, so our answer is plausible.
(b) For an atom to have no overall charge (0 net charge):
total positive charge + total negative charge = 0
total positive charge = 26 × +1 = +26
total negative charge = 26 × -1 = -26
+26 + -26 = 0
so our answer is plausible
- State your solution to the problem "number of electrons in the atom":
Number of electrons = 26
