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(D) 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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(D) 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,the principal quantum number $n$ decreases,so the radius $r$ decreases.The kinetic energy is $K.E. = \frac{kZe^2}{2r}$. Since $r$ decreases,$K.E.$ increases.The potential energy is $P.E. = -\frac{kZe^2}{r}$. Since $r$ decreases,the magnitude of $P.E.$ increases,meaning $P.E.$ becomes more negative (decreases).The total energy is $T.E. = -\frac{kZe^2}{2r}$. Since $r$ decreases,the magnitude of $T.E.$ increases,meaning $T.E.$ 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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