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Suppose an electron is attracted toward ...

Suppose an electron is attracted toward 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 ?

A

`T_(n)` independent of n , `r_(n) prop n `

B

`T_(n) prop 1/n , r_(n) prop n `

C

`T_(n) prop 1/n , r_(n) prop n^(2)`

D

`T_(n) prop 1/(n^(2)) , r_(n) prop n^(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
As `k/r =(mv^(2))/r and L - (nh)/(2pi) rArr mv_(n)r_(n)=(nh)/(2pi)`
`rArr m((nh)/(2pimr_(n)))^(2) = k rArr r_(n) prop n `
T = kinetic energy = `1/2 mv_(n)^(2)`
`rArr T_(n) = 1/2 m((nh)/(2pimr_(n)))^(2)rArrT_(n)prop (n^(2))/(r_(n)^(2))`
`rArr T_(n) prop n^(0) " " (as r_(n) prop n)` .
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