Question

Calculate the speed of electron revolving around the nucleus of a hydrogen atom in order that it may not be pulled into the nucleus by electrostatic attraction

Answer 1

Answer:

see equate the centrfugalal force and the electrostatic force of attraction kze^2/r^2=mv^2/r

and also

mvr=nh/2pie (angilarmomentum)

and divide these two equations and u)( get the speed directly

thanks

Answer 2

The value of velocity is equal to 4πke²/nh

First we will equate the centrifugal force equation and the electrostatic force of attraction equation-

kze²/r² = 1/2 mv²/r

=> 2kze²/r = mv² -------(1)

The angular momentum of the electron in the nth orbital of the hydrogen atom,mvr = nh/2π

=> r = nh/2πmv

Put the value of r in the equation (1)

=> 2kze²/(nh/2πmv) = mv²

=> 2kze²×2πmv / nh = mv²

=> 4πkze²/nh = v

=> v = 4πke²/nh [z = 1 , for hydrogen atom]

The value of v is equal to 4πke²/nh