Q. 195.0( 4 Votes )

Find the speed of the electron in the ground state of a hydrogen atom. The description of ground state is given in the previous problem.

Answer :

Given:


Magnitude of charge on both proton and electron,


The radius of the circular orbit,


Mass of electron ,



The radius of the circular orbit is the distance between the electron and the proton.


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Formula used:


By Coulomb’s law, the electric force is given by:



Where ϵ0 is the permittivity of free space


q1 and q2 are the magnitude of charges


r is the distance of separation between the charges


(Here, )


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The magnitude of electric force is given by:




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Formula used:


Centripetal force is given by



Where m is the mass if the object, v is the speed of the object and r is the radius of the circular path.


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Let Fc be the centripetal force on the electron.



Now, the electric force acts as centripetal force.


Hence,



Substituting (1) and rearranging, we get



Putting the values in the above formula, we get



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