Soppose potential energy between electronand proton at seperation `r` is given by `U = klog r, where k` is a constant. For such a hypothetical hydrogen atom , calculate the radins of nth Bohr and its energy level

Explanation

`U=k "log"_(e) r`
`F=-(dU)/(dr)=-(k)/(r )`
`(mv^(2))/(r )=(k)/(r )` " "……(i)
`mvr=(nh)/(2pi)` " " ……(ii)
From (i),`vsqrt((k)/(m))` "in" (ii)
` msqrt((k)/(m))r=(nh)/(2pi)`
"Squaring both sides, we get "
`m^(2)(k)/(m)r^(2)=(n^(2)h^(2))/(4pi^(2))`
`r=r_(n)=((n^(2)h^(2))/(4pi^(2)km))^(1/2)`
"Total energy"
`E=K+U=(1)/(2)mv^(2)+U`
`=(k)/(2)+k "log"_(e)((n^(2)h^(2))/(4pi^(2)km))^(1/2)`