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(C) For a hydrogen-like atom,the radius of the orbit is given by $r_n \propto n^2$. As the electron transitions from an excited state to the ground st

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its kinetic energy increases but potential energy and total energy decrease

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(C) For a hydrogen-like atom,the radius of the orbit is given by $r_n \propto n^2$. As the electron transitions from an excited state to the ground state,$n$ decreases,so the radius $r$ decreases.The kinetic energy is given by $K.E. = \frac{kZe^2}{2r}$. Since $r$ decreases,the kinetic energy increases.The potential energy is given by $P.E. = -\frac{kZe^2}{r}$. Since $r$ decreases,the magnitude of the negative potential energy increases,meaning the potential energy becomes more negative (decreases).The total energy is given by $T.E. = -\frac{kZe^2}{2r}$. Since $r$ decreases,the total energy becomes more negative (decreases).Therefore,kinetic energy increases,while potential energy and total energy decrease.

As an electron makes a transition from an excited state to the ground state of a hydrogen-like atom/ion:

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