suppose an electron is attracted towards the origin by a force `k//r`, where k is a constant and r is the distance of the electron form the origin. By applying bohr model to this system, the radius of `n^th` orbit of the electron is found to be `r_n` and the kinetic energy of the electron is found to be `T_n` Then which of the following is true ?

Options

A. `T_(n )` indepnednt of `n,r_(n)prop n `
B. `T_(n)prop(1)/(n),r_(n)propn`
C. ` T_(n)prop(1)/(n), r_(n)propn ^(2)`
D. `T_(n)prop(1)/(n^(2)),r_(n)propn^(2)`

Answer

A

Explanation

Accroding to Bohr theory, `mvr=n(hc)/(2pi)rArrv=(nh)/(2pimr)`
`and " " (mv^(2))/(r)prop(k)/(r)rArr(m)/(r)((n^(2)h^(2))/(4pi^(2)m^(2)r^(2)))prop(k)/(r)`
`rArr" " r_(n)propn`
Kinetic energy of the electron
`" " T=(1)/(2)mv^(2)=(1)/(2)m((n^(2)h^(2))/(4pi^(2)m^(2)r^(2)))rArrT_(n)prop(n^(2))/(r^(2))`
But as `prop` therefore `Tpropn^(0)`