in a hypothetical atom, potential energy beteen electron and proton at distance 'r' is given by (-ke24r3) where k is constant . suppose bohr model is valid and n is principal quatum number , then total energy is proportional to ;
(Ans) n6
71You just need to rework the way the usual proportionality relationship is derived ie., E prop. to z2n2
Here, You are given the Potential and hence you know the force between between the concerned particles. You can get then the new relationship.
However, I'll try to think of any other method too.
21Potential energy is prop. to 1/r3
potential energy =Force.∂r
Force is prop=1/r4
The other force is mv2/r
Now, as Bohrs hypothesis is true,mvr=nh/2Ï€
By balancing forces, 1/r4 is prop. to v2/r [and v is prop. to n/r]
therefore 1/r is prop to n2
therefore total energy is prop. to potential energy is prop to 1/r3 is prop to n6
