Seemingly Simple - How Many Orbits? (Rotational Kinematics)

In summary, the question discusses the Bohr model of the hydrogen atom and the motion of the electron in the n=2 orbit. It asks for the number of orbits the electron makes around the proton per second. The correct angular velocity is 5.15e15 rad/s, but converting to revolutions per second yields an incorrect answer. The computer indicates that the conversion is incorrect and there is no other solution.
  • #1
kmj9k
16
0
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!
 
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  • #2
kmj9k said:
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.
 
  • #3


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.
 

Related to Seemingly Simple - How Many Orbits? (Rotational Kinematics)

1. What is rotational kinematics?

Rotational kinematics is a branch of physics that studies the motion of objects as they rotate around a fixed axis. It deals with quantities such as angular velocity, angular acceleration, and torque.

2. What is the difference between linear and rotational kinematics?

The main difference between linear and rotational kinematics is the type of motion that is being studied. Linear kinematics deals with the motion of objects along a straight line, while rotational kinematics deals with the motion of objects as they rotate around a fixed axis.

3. What is the relationship between angular velocity and linear velocity?

Angular velocity and linear velocity are directly related to each other. The linear velocity of a point on a rotating object is equal to the angular velocity of the object multiplied by the distance from the axis of rotation to the point.

4. How is rotational kinematics used in real life?

Rotational kinematics is used in many real-life applications, such as designing and analyzing the motion of rotating machinery, understanding the dynamics of vehicles and other moving objects, and studying the movements of celestial bodies.

5. What is the equation for calculating the number of orbits in rotational kinematics?

The equation for calculating the number of orbits in rotational kinematics is N = ωt / 2π, where N is the number of orbits, ω is the angular velocity, and t is the time. This equation assumes that the object is moving at a constant angular velocity.

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