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

Question

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

${T_n} \propto {1 \over {{n^2}}},{r_n} \propto {n^2}$

${T_n}$ independent of $n,{r_n} \propto n$

${T_n} \propto {1 \over n},{r_n} \propto n$

${T_n} \propto {1 \over n},{r_n} \propto {n^2}$

Solution

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