Suppose in the Bohar's model of H-atom, instead of electron forec, some other force is acting between nucleus & electronwhich cause thepotential energy to vary as -(K)/(6r^(6)). Assuing Bohar's quantizationof angular momentum.(Given : Mass o fan electron =m) (i) Derive expression for radiusof n^(th) orbit(ii)Given the expression to obitain energy of such a hydpotheticalatoms .

Suppose in the Bohar's model of H-atom, instead of electron forec, som

1.	Suppose in the Bohar's model of H-atom, instead of electron forec, some other force is acting between nucleus & electronwhich cause thepotential energy to vary as -(K)/(6r^(6)). Assuing Bohar's quantizationof angular momentum.(Given : Mass o fan electron =m) (i) Derive expression for radiusof n^(th) orbit(ii)Given the expression to obitain energy of such a hydpotheticalatoms .
Answer» Solution :`(mv^(2))/(r)=(k)/(r^(7))"".......(1)""U=-(k)/(6r^(6))` `mvr=(NH)/(2PI)……..(2)""F=(du)/(dr)=-((-6)r^(-7)k)/(6)` "subsituting" `V=(nh)/(2pimr)," inequation (1)"` `m((nh)/(2pimr))^(2)=(k)/(r^(6))` `r^(4)=(4pi^(2)mk)/(N^(2)h^(2))""rArr=((2pi)/(n h))^(1//2)(mK)^(1//4)` T.E`=(1)/(2)mv^(2)+(-(k)/(6r^(6)))` `=(K)/(2r^(6))-(K)/(6r^(6))`=`(k)/(r^(6))[(1)/(2)-(1)/(6)]=(k)/(r^(6))[(3-1)/(6)]` T.E.`=(k)/(3R^(6))`=`(k)/(3((2pi)/(nh))^(6//2)(mk)^(6//4))`=`((n^(3)h^(3))/(24pi^(3)))((1)/(m^(3//2)sqrtK))`