Assume that there is no repulsive force between the electrons in an atom but the force between positive and negative charges is given by Coulomb’s law as usual. Under such circumstances, calculate the ground state energy of a He-atom.

Question

Philoid · Accepted Answer

Consider helium atom,

centripetal force on the electron due to nucleus=

Electrostatic force on electron due to nucleus=

Now centripetal force allows the electron to revolve in the orbit, thus balancing the forces,

⇒

---(1),

where z = atomic number of atom

m is mass of electron

v is the velocity of the electron on nth orbit

in permittivity in vacuum

And r is the Bohr radius

Now from orbital angular momentum equation for nth orbit,

-(2)

Kinetic energy of electron in the nth orbit =

Potential energy of the electron in the nth orbit =

Now total energy,

Putting 1 in above equation, we get

For helium atom Z=2

∴ ground state energy for helium atom is 54.4Ev