[ssssss]

I am studying Bohrs atomic model i got few problems with it.I will be thatnkful whomesoever clear my doubts.

1.Total energy of electron in an orbit is=-13.6eV/n² x Z².

Here Z is the atomic number of the system and n is the orbit number.

Now i read my book,it said that this is the sum of the Total Kinetic and Total potential Energy of electron in that orbit.And my book does not mention what is this Kinetic and Potential Energy of the electron in the orbit.Can you explain what are these energies and How to derive their value?

2.Why does Bohrs atomic model fails to explain the spectrum of elements with more than 1 electrons?

3.How to calculate the angular frequency of an electron revolving in an specific orbit?

[Mitch]

2. Because the equation fails to incorporate the electon-electron repulsion from the added electron.

[Demotivator]

1) E = (1/2)mv² - ke²/r   (sum of kinetic(Newton's law) and potential (Coulomb's law) energy.
now, angular momentum is mvr
Bohr  equates this with nh/2pi
so mvr = nh/2(pi)
third assumption: centrifugal force = centripetal force:
mv²/r = e²/r²
by using the above two equations and substituting for r,  v becomes:
v=2(pi)e²/nh  
where e is the charge like Z.
Square the resulting v and use it below:
 kinetic energy = (1/2)mv²

3) are you sure you don't mean angular momentum?
   nh/2(pi)
n is the orbit , h is planck's constant.

[ssssss]

1) E = (1/2)mv² - ke²/r   (sum of kinetic(Newton's law) and potential (Coulomb's law) energy.
now, angular momentum is mvr
Bohr  equates this with nh/2pi
so mvr = nh/2(pi)
third assumption: centrifugal force = centripetal force:
mv²/r = e²/r²
by using the above two equations and substituting for r,  v becomes:
v=2(pi)e²/nh  
where e is the charge like Z.
Square the resulting v and use it below:
 kinetic energy = (1/2)mv²

3) are you sure you don't mean angular momentum?
   nh/2(pi)
n is the orbit , h is planck's constant.

Oh very thanks to you.But can you tell me why we take the potential energy negative[-ke²/2].And yes i mean to say angular frequency.

[ssssss]

2. Because the equation fails to incorporate the electon-electron repulsion from the added electron.

Is there any way we can modify this model by taking the repulsion of eS into account.

[Demotivator]

e2/r is not the force between two electrons. It is between a nucleus of charge +Ze (in coulombs) and an electron of opposite charge -e (in coulombs). When multiplied the result is -Ze2. Assuming a one proton atom Z = 1, it reduces to -e²/r. The negative sign can be taken to indicate that the potential energy is the result of an attractive force. Potential energy increases and approaches zero as an electron approaches the outer limit of an atom.

Angular or orbital frequency is the number of orbital revolutions an electron makes in a second.
For a nucleus of atomic number Z:
  6.57968 x 10¹⁵Z²/n³ Herz

[ssssss]

e2/r is not the force between two electrons. It is between a nucleus of charge +Ze (in coulombs) and an electron of opposite charge -e (in coulombs). When multiplied the result is -Ze2. Assuming a one proton atom Z = 1, it reduces to -e²/r. The negative sign can be taken to indicate that the potential energy is the result of an attractive force. Potential energy increases and approaches zero as an electron approaches the outer limit of an atom.

Angular or orbital frequency is the number of orbital revolutions an electron makes in a second.
For a nucleus of atomic number Z:
  6.57968 x 10¹⁵Z²/n³ Herz

Thank for the knowledge.Now i think my doubts on Bohrs model is clear.