Calculating Centripetal Acceleration and Gravitational Force in a Hydrogen Atom

In summary, the mass of an electron is 9 x 10-31 kg, the mass of a proton is 1.7 x 10-27 kg, and the electron and proton are about 1.0 x 10-10 m apart in a hydrogen atom. The force of gravity between the proton and electron is 1.02051 x 10^-47 N, the centripetal acceleration of the electron is 5.508 x 10^-27 N/s, and the electrical force provides the centripetal force.
  • #1
tuffshorty
11
0

Homework Statement



The mass of an electron is 9 x 10-31 kg. The mass of a proton is 1.7 x 10-27 kg. The proton and electron are about 1.0 x 10-10 m apart in a hydrogen atom. What force of gravitation exists between the proton and the electron of a hydrogen atom? What is the centripetal acceleration of the electron?

Homework Equations


Fg = G*m1*m2/d^2
* Fg is the magnitude of the gravitational force between the two point masses,
* G is the gravitational constant,
* m1 is the mass of the first point mass,
* m2 is the mass of the second point mass,
* r is the distance between the two point masses.

ar = v2 / r

ar is centripetal acceleration
v is velocity in meters per second,
r is the radius of the circle in meters

The Attempt at a Solution



I plugged in the infomation to find the gravitational force and got 1.02051 x 10^-47
but it doesn't give us the nessicary information to find the centripetal acceleration... I don't think.. can anyone help me with this?
 
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  • #2
What provides the centripetal force?
 
  • #3
It rotating around the hydrogen atom I think...
 
  • #4
tuffshorty said:
It rotating around the hydrogen atom I think...
The electron "orbits" the proton. Again, what provides the centripetal force?
 
  • #5
I suppose I am not sure what you mean.. or what provides it... that is all the question said...
 
  • #6
What force holds the atom together? (It's not gravity.)
 
  • #7
The electrical charge of the atom?
 
  • #8
tuffshorty said:
The electrical charge of the atom?
Right. The electric force provides the centripetal force. How much is the electrical force? (Hint: Coulomb's law) Once you have the centripetal force, use Newton's 2nd law to find the acceleration.
 
  • #9
5.508 x 10^-27 N is what i got when i plugged it in...
and for the acceleration i got 6120 meter/second^2
 
Last edited:
  • #10
tuffshorty said:
5.508 x 10^-27 N is what i got when i plugged it in...
and for the acceleration i got 6120 meter/second^2
Please show how you made those calculations.
 

Related to Calculating Centripetal Acceleration and Gravitational Force in a Hydrogen Atom

1. What is centripetal acceleration?

Centripetal acceleration is the acceleration experienced by an object moving in a circular path. It is directed towards the center of the circle and is responsible for keeping the object moving in the circular path.

2. How is centripetal acceleration calculated?

The formula for centripetal acceleration is a= v^2/r, where a is the centripetal acceleration, v is the velocity of the object, and r is the radius of the circular path.

3. What is the difference between centripetal acceleration and centrifugal force?

Centripetal acceleration is the acceleration required to keep an object moving in a circular path, while centrifugal force is a fictitious force that appears to act on an object moving in a circular path.

4. How does centripetal acceleration affect the motion of an object?

Centripetal acceleration causes a change in the direction of an object's velocity, but not its speed. This means that the object's speed remains constant, but its direction changes constantly, resulting in circular motion.

5. What are some real-life examples of centripetal acceleration?

Some common examples of centripetal acceleration include the motion of a car around a curve, the rotation of the Earth around the Sun, and the rotation of a merry-go-round. Any object that moves in a circular path experiences centripetal acceleration.

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