Suppose an electron is attracted towards the origin by a force k/r… | JEE Main 2008 (AIEEE)

Q117JEE Main 2008 · AIEEEDifficult

Bohr Model: Orbits, Speed & Angular Momentum

Suppose an electron is attracted towards the origin by a force $\frac{k}{r}$ 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?

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Answer: (b)

$\frac{mv^2}{r} = \frac{k}{r} \Rightarrow mv^2 = k$ , so $v$ is constant.
$T = \frac{1}{2}mv^2 = \frac{k}{2}$ , independent of $n$ .
Bohr condition: $mvr = \frac{nh}{2\pi}$ with constant $v$ , so $r_n \propto n$ .
So the answer is (b) $T_n$ independent of $n$ , $r_n \propto n$ .

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