In a hypothetical model of an atoms following Bohr's theory, the potential energy is given by potential energy `=-(Ke^(2))/(4r^(4))`. Which of the following options will be correct ? (Symbols have usual meaning)

Options

A. KE=-PE
B. `r=(nhe)/(4pi)sqrt(K/m)`
C. `v=(n^(2)h^(2))/(4pi^(2)m^(3//2) esqrtK)`
D. `TE =(-Ke^(2))/(2r^(4))`

Answer

C

Explanation

`PE=-(Ke^(2))/(4r^(4))`
Force `=-(dE)/(4r)=-(4Ke^(2))/(r^(5)) =(mv^(2))/r`
`mvr=(nh)/(2pi)`
`(ke^(2))/(r^(5))=m/r((n^(2)h^(2))/(4pi^(2)m^(2)r^(2)))`
`r^(2)=(4pi^(2)m ke^(2))/(n^(2)h^(2)) rArr (2pie)/(nh) sqrt(mk)`
`v=(nh)/*(2pim) . (nh)/(2piesqrt(mk))=(n^(2)h^(2))/(4pi^(2)m^(3//2) esqrt(K))`