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 8.2 x 10^-8 N. How many revolutions per second does the electron make?

Verified step by step guidance

1. Calculate the centripetal force required to keep the electron in circular motion. Use the formula for centripetal force, $F_c=\frac{m{v}^2}{r}$, where $m$ is the mass of the electron, $v$ is the velocity of the electron, and $r$ is the radius of the orbit.
2. Set the centripetal force equal to the electric force given, since the electric force is providing the necessary centripetal force to keep the electron in orbit. Solve for the velocity $v$ of the electron using the equation $8.2\times {10}^{-8}\text{N}=\frac{9.1\times {10}^{-31}\text{kg}\times v^2}{5.3\times {10}^{-11}\text{m}}$.
3. Calculate the circumference of the electron's orbit using the formula for the circumference of a circle, $C=2\pi r$, where $r$ is the radius of the orbit.
4. Determine the time it takes for one complete revolution by dividing the circumference by the velocity, using the formula $T=\frac{C}{v}$.
5. Finally, calculate the number of revolutions per second by taking the reciprocal of the time for one revolution, using the formula $\text{Revolutions per second}=\frac{1}{T}$.

Key Concepts

Centripetal Force

Centripetal force is the net force that acts on an object moving in a circular path, directed towards the center of the circle. In the context of the Bohr model, the electric force between the proton and electron provides the necessary centripetal force to keep the electron in its circular orbit. This relationship is crucial for determining the electron's motion and frequency of revolutions.

Electric Force

Electric force is the attractive or repulsive interaction between charged particles, described by Coulomb's law. In the hydrogen atom, the proton (positively charged) exerts an electric force on the electron (negatively charged), which is responsible for the electron's circular motion around the nucleus. Understanding this force is essential for calculating the dynamics of the electron's orbit.

Angular Velocity

Angular velocity is a measure of how quickly an object rotates around a central point, expressed in radians per second or revolutions per second. In the case of the electron in the Bohr model, the angular velocity can be derived from the balance of centripetal force and the electric force acting on the electron. This concept is key to determining the number of revolutions the electron makes in a given time frame.