How Do You Calculate Electron Force and Speed in Bohr's Atom Model?

[suhaskowshik_92]

Homework Statement

A bohr`s model of an atom,taking the radius of the hydrogen atom as r=5.29*10^-11m ,find the strength of the force on the electron,its centripetal acceleraton and itsorbital speed.

Homework Equations

The Attempt at a Solution

 

[Astronuc]

Please show some work.

Write the equation for the Coulomb force between electron and proton. That has to be balanced by the centripetal force, if one assumes classical mechanics.

http://hyperphysics.phy-astr.gsu.edu/hbase/bohr.html#c3

 

[m2003]

Electrostatics is a branch of physics that deals with the study of electric charges at rest and their interactions. In the given homework statement, we are asked to find the strength of the force, centripetal acceleration, and orbital speed of an electron in a Bohr's model of an atom, assuming the radius of the hydrogen atom as 5.29*10^-11m. To solve this problem, we can use the equations for Coulomb's Law, centripetal force, and centripetal acceleration.

First, we can calculate the strength of the force on the electron using Coulomb's Law, which states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. In this case, the distance between the electron and the nucleus is equal to the radius of the hydrogen atom, which is given as 5.29*10^-11m. The charge of an electron is -1.6*10^-19 C and the charge of a proton (in the nucleus) is +1.6*10^-19 C. Plugging these values into the equation, we get the force on the electron as 8.99*10^9 N.

Next, we can calculate the centripetal acceleration of the electron using the equation F=ma, where F is the force on the electron and m is its mass. The mass of an electron is approximately 9.11*10^-31 kg. Plugging in the values, we get the centripetal acceleration as 9.83*10^22 m/s^2.

Finally, we can calculate the orbital speed of the electron using the equation v=√(rω), where r is the radius of the orbit and ω is the angular velocity. In the Bohr's model, the angular velocity is given as v=rω, where v is the speed of the electron and r is the radius of the orbit. Substituting the values, we get the orbital speed as 2.19*10^6 m/s.

In conclusion, by using the equations for Coulomb's Law, centripetal force, and centripetal acceleration, we can determine the strength of the force, centripetal acceleration, and orbital speed of an electron in a Bohr's model of an atom.