1.

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 from the origin. By applying Bohr model to this system, the radius of the n^(th) orbital of the electron is found to be r_(n) and the kinetic energy of the electron to be T_(n). Then which of the following is true?

Answer»

`T_(n)prop(1)/(n),r_(n)propn^(2)`
`T_(n)prop(1)/(n^(2)),r_(n)propn^(2)`
`T_(n)` is independent then `n,r_(n)propn`
`T_(n)prop(1)/(n),r_(n)propn`

Solution :If the velocity of an electron in `n^(TH)` orbit is `v_(n)`, then the centripetal FORCE = the force on electron.
`:.(mv_(n)^(2))/(r_(n))=(K)/(r_(n))`
`:.v_(n)^(2)=(K)/(m)`
`T_(n)=(1)/(2)m((K)/(m))`
`:.T_(n)=(K)/(2)`
Now KINETIC energy `=(1)/(2)mv_(n)^(2)`
Here, there is no n TERM, so the kinetic energy is independent then n.
From Bohr.s hypothesis, the angular momentum
`mv_(n)r_(n)=(nh)/(2pi)`
`:.r_(n)=(nh)/(2pimv_(n))`
`:.r_(n)=(nh)/(2pimxsqrt((k)/(m))):.r_(n)=(nh)/(2pisqrt(mk))`
`:.r_(n)propn`


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