Question

The hydrogen atom consists of a proton of mass 1.67x10-27 kg and an orbiting electron of mass 9.11x10-31 kg. In one of its orbits, the electron is 5.3x10-11 m from the proton. What is the mutual attractive gravitational force between the electron and the proton?

Answer 1

The mass of the proton,
m
p
=
9.11
×
10
−
31
k
g
The mass of the electron,
m
e
=
1.67
×
10
−
27
k
g
The distance between them,
r
=
5.3
×
10
−
11
m


The gravitational force between two objects of mass,
m
1
, and
m
2
, separated by a distance,
r
, is given by the following equation:

F
=
G
m
1
m
2
r
2

Here,

G
=
6.67
×
10
−
11
m
3
/
k
g
.
s
2
is the gravitational constant.
On plugging the given values, we have:

F
=
6.67
×
10
−
11
×
1.67
×
10
−
27
×
9.11
×
10
−
31
(
5.3
×
10
−
11
)
2
=
3.61
×
10
−
47
N

Answer 2

The gravitational force of attraction between the proton and the electron is 3.61×10⁻⁴⁷ N.

Gravitational force:

The mass of the proton is M = 1.67×10⁻²⁷kg

The mass of the electron is m = 9.11×10⁻³¹ kg

The distance of the electron from the proton is r = 5.3×10⁻¹¹m

The gravitational force of attraction between the proton and the electron is given by:

F = GMm/r²

where G is the gravitational constant

F = (6.67×10⁻¹¹)(1.67×10⁻²⁷)(9.11×10⁻³¹)/(5.3×10⁻¹¹)² N

F = 3.61×10⁻⁴⁷ N

Learn more about gravitational force:

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