Answer:
In the standard model of particle physics, baryons are composite particles made up of three quarks. Quarks come in six different flavors (up, down, charm, strange, top, and bottom), each with its own electric charge. The electric charges of the quarks are as follows:
Up quark (
�
u):
+
2
3
+
3
2
e
Down quark (
�
d):
−
1
3
−
3
1
e
Charm quark (
�
c):
+
2
3
+
3
2
e
Strange quark (
�
s):
−
1
3
−
3
1
e
Top quark (
�
t):
+
2
3
+
3
2
e
Bottom quark (
�
b):
−
1
3
−
3
1
e
Here,
�
e represents the elementary charge, approximately
1.602
×
1
0
−
19
1.602×10
−19
Coulombs.
Now, let's consider combinations of three quarks to form baryons:
Baryons with Different Flavor Quarks:
When you combine three quarks with different flavors (e.g.,
�
�
�
uud), their charges add up algebraically.
For example, for a
�
�
�
uud combination, the total charge is
(
2
3
+
2
3
−
1
3
)
�
=
3
3
�
=
1
�
(
3
2
+
3
2
−
3
1
)e=
3
3
e=1e.
Similarly, any combination of different flavor quarks in a baryon will result in charges that are multiples of the elementary charge (
�
e), which are integral charges.
Baryons with Two Quarks of One Flavor and One of Another Flavor:
When you have two quarks of one flavor and one of another flavor in a baryon (e.g.,
�
�
�
uud,
�
�
�
uds), the charges will also add up to an integral charge.
For example, for a
�
�
�
uds combination, the total charge is
(
2
3
−
1
3
−
1
3
)
�
=
0
�
(
3
2
−
3
1
−
3
1
)e=0e.
This also applies to other combinations with two quarks of one flavor and one of another flavor.
Baryons with Three Quarks of the Same Flavor:
When you have three quarks of the same flavor in a baryon (e.g.,
�
�
�
uuu or
�
�
�
ddd), the charges will add up to zero.
For example, for a
�
�
�
uuu combination, the total charge is
(
2
3
+
2
3
+
2
3
)
�
=
2
�
−
1
�
=
1
�
(
3
2
+
3
2
+
3
2
)e=2e−1e=1e.
Similarly, for a
�
�
�
ddd combination, the total charge is
(
−
1
3
−
1
3
−
1
3
)
�
=
−
1
�
(−
3
1
−
3
1
−
3
1
)e=−1e.
Since all combinations of three quarks to form baryons either produce integral charges or zero charges, baryons must have integral charges. This property is a fundamental aspect of the quark model and is a key feature of the strong force in particle physics.