Seemingly Simple - How Many Orbits? (Rotational Kinematics)

[kmj9k]

This is the latest question I've been stuck on.

The Bohr model of the hydrogen atom pictures the electron as a tiny particle moving in a circular orbit about a stationary proton. In the n=2 orbit, the distance from the proton to the electron is 21.16e-11 m , and the linear speed of the electron is 1.09e6 m/s.

How many orbits about the proton does it make each second?

Now, I found the angular velocity of the electron and got that correct: 5.15e15 rad/s. Now, to find the # of orbits, shouldn't I just convert to revolutions per second, which is 8.09e15 rev/s? The computer tells me I'm wrong, however, but I don't know what I could do differently.

Again, I appreciate your time!

 

[OlderDan]

This is the latest question I've been stuck on.

The Bohr model of the hydrogen atom pictures the electron as a tiny particle moving in a circular orbit about a stationary proton. In the n=2 orbit, the distance from the proton to the electron is 21.16e-11 m , and the linear speed of the electron is 1.09e6 m/s.

How many orbits about the proton does it make each second?

Now, I found the angular velocity of the electron and got that correct: 5.15e15 rad/s. Now, to find the # of orbits, shouldn't I just convert to revolutions per second, which is 8.09e15 rev/s? The computer tells me I'm wrong, however, but I don't know what I could do differently.

Again, I appreciate your time!

I promise you that it is impossible to do more full revolutions than radians in the same amount of time. Your angular velocity looks good; your conversion does not.

 

[kyle8921]

It seems that you have correctly calculated the angular velocity of the electron and converted it to revolutions per second. However, it is important to note that in the Bohr model, the electron is not actually moving in a circular orbit around the proton. It is actually in a state of constant motion, known as a standing wave, which means that it is not actually making any orbits around the proton. Therefore, the concept of revolutions per second does not apply in this scenario.

Additionally, the Bohr model is a simplified model and does not accurately represent the behavior of electrons in atoms. In reality, electrons exist in orbitals, which are regions of space where the probability of finding an electron is high. These orbitals do not have a defined path or speed for the electron, making it impossible to determine the number of orbits the electron is making in a given time period.

In conclusion, while the concept of orbits is helpful in understanding the behavior of electrons in atoms, it is not applicable in the context of the Bohr model and the question of how many orbits an electron makes per second cannot be answered accurately. It is important to consider the limitations of models and to continue exploring and learning about the complex behavior of atoms and their constituent particles.