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 $n^{\text{th}}$ 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? (1) $T_n \propto 1/n^{2}, \quad r_n \propto n^{2}$ (2) $T_n$ independent of $n, \quad r_n \propto n$ (3) $T_n \propto 1/n, \quad r_n \propto n$ (4) $T_n \propto 1/n, \quad r_n \propto n^{2}$
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 $n^{\text{th}}$ 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?\\
(1) $T_n \propto 1/n^{2}, \quad r_n \propto n^{2}$\\
(2) $T_n$ independent of $n, \quad r_n \propto n$\\
(3) $T_n \propto 1/n, \quad r_n \propto n$\\
(4) $T_n \propto 1/n, \quad r_n \propto n^{2}$