Dynamics of uniform circular motion and bohr model

In summary, the problem is about calculating the number of revolutions per second made by an electron in the Bohr model of the hydrogen atom. The electron has a mass of 9.1 x 10^-31 kg and orbits a proton at a distance of 5.3 x 10^-11 m. With an electric force of 9.2 x 10^-8 N, the velocity of the electron can be calculated using the formula v = sqrt((distance * force)/ mass). This results in a velocity of 1636802 m/s. The angular velocity can then be found using the formula w = v / r, which gives a value of 3.084 x 10^23 rad/s. Finally, the
  • #1
quick
42
0
In the Bohr model of the hydrogen atom, an electron (mass m = 9.1 x 10^-31 kg) orbits a proton at a distance of 5.3 x 10^-11 m. The proton pulls on the electron with an electric force of 9.2 x 10^-8 N. How many revolutions per second does the electron make?

can someone help me solve this problem?
 
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  • #2
first of all
:mad: :mad: :mad:

SHOW SOME WORK we're not here to do your work for you!

Secondly F = m V^2 / R

Secondly distance / velocity = time

what is the distance traveled by this electron ? Is it a straight line or something else? If it something else , isn't htat something else defined by some formula?

The time given in the above formula represents something, what does it represent?

All the clues are here, show some work and i'd have been more helpful
 
  • #3
sorry i had done the problem but it was incorrect so i figured i would start from scratch. anyways i did complete some parts that are still useful. using F = mv^2/r
i got the velocity = sqrt(F*r/m) so v = 1636802. for radius am i correct in assuming that the distance given is the diameter? if so, i got a time of 3.23 x 10^-17 s. the electron is orbiting a proton so do i use the time as the period and compute the velocity using v = 2*pi*r/T(period) ?
 
  • #4
ok i figured it out. thanks for your hints. basically i didn't realize that the distance given was the actual distance instead of my dividing it by two to get a radius. so i just used v = sqrt((distance * force)/ mass) to get the velocity and then to get the angular velocity i just did velocity / distance. then converted from radians to rev/s.
 
  • #5
quick said:
sorry i had done the problem but it was incorrect so i figured i would start from scratch. anyways i did complete some parts that are still useful. using F = mv^2/r
i got the velocity = sqrt(F*r/m) so v = 1636802. for radius am i correct in assuming that the distance given is the diameter? if so, i got a time of 3.23 x 10^-17 s. the electron is orbiting a proton so do i use the time as the period and compute the velocity using v = 2*pi*r/T(period) ?

exactly

period is given by 2 pi r / v or if you care for angular velocity w = v/ r then T = 2 pi / w and you're done like dinner
 

Related to Dynamics of uniform circular motion and bohr model

1. What is uniform circular motion?

Uniform circular motion refers to the motion of an object that moves in a circular path at a constant speed, with the direction of motion constantly changing.

2. How is uniform circular motion different from linear motion?

In uniform circular motion, the speed of the object remains constant, but the direction of motion changes. In linear motion, the object moves in a straight line with no change in direction.

3. What is the Bohr model?

The Bohr model is a simplified model of the atom proposed by Niels Bohr in 1913. It states that electrons orbit the nucleus in fixed energy levels, and can jump between these levels by absorbing or emitting energy.

4. How does the Bohr model explain the stability of atoms?

The Bohr model explains the stability of atoms by proposing that the electrons are in constant motion in a fixed energy level, preventing them from falling into the nucleus. It also accounts for the discrete energy levels observed in atomic spectra.

5. What is the relationship between circular motion and the Bohr model?

The Bohr model is based on the concept of circular motion, as the electrons are thought to move in circular orbits around the nucleus. This relationship is used to explain the spectral lines observed in atoms and to calculate the energy levels of the electrons.

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