How far apart must two protons be if the repulsive force acting on either one is equal to its weight?
Answers
Explanation:
We will need the following constants to solve this problem:
g
=
9.8
m
/
s
2
is the acceleration due to gravity
m
=
1.67
×
10
−
27
k
g
is the mass of a proton
q
=
1.602
×
10
−
19
C
is the charge of a proton
We first calculate the weight of a proton. Since the reference proton is on Earth's surface, we use:
F
=
m
g
We substitute:
F
=
(
1.67
×
10
−
27
k
g
)
(
9.8
m
/
s
2
)
We will get:
F
=
1.6366
×
10
−
26
N
The electrostatic force between the protons can be calculated using Coulomb's law:
F
=
k
q
1
q
2
r
2
Since we are dealing with two protons, we set:
q
1
=
q
2
=
q
We simplify:
F
=
k
q
2
r
2
We isolate the distance r:
r
=
√
k
q
2
F
Since the repulsive force must be equal to the weight, we set the force F to be equal to our derived weight. We substitute:
r
=
√
(
9
×
10
9
N
m
2
/
C
2
)
(
1.602
×
10
−
19
C
)
2
1.6366
×
10
−
26
N
We get:
r
=
0.12
m