If the speed of the electron in a hydrogen atom orbit of principal quantum number n be V, then the curve showing variation of V with n is:

Options

A. a straight line
B. a parabola
C. a rectangular hyperbola
D. on helix.

Answer

C

Explanation

The Columb.s attraction provides the necessary centripetal force the nucleus and the electron
`(mv^(2))/(r_(n))=(1)/(4pi epsi_(0)) ((Ze).e)/(r_(n)^(2))`
`mv^(2) r_(n)=(Ze^(2))/(4pi epsi_(0))`
`mv^(2)r_(n)=(Ze^(2))/(4pi epsi_(0))..........(1)`
Bohr.s quantum condition gives
`mvr_(n)=(nh)/(2pi) ..........(2)`
Dividing eq. (1) by (2),
`(mv^(2)r_(n))/(mv r_(n))=((Ze^(2))/(4pi epsi_(0)))/((nh)/(2pi))`
`v=(Ze^(2))/(2n epsi_(0)h)`
`v xx n =(Ze^(2))/(2epsi_(0) h)="constant"`
i.e. `v xx n ="constant" .......(3)`
Equation (3) represent a reactangular hyperbola.