Match List-I with List-II regarding the energies of an electron in...

For an electron in a hydrogen-like atom, the relationships between kinetic energy (KE), potential energy (PE), and total energy (TE) are:

$\text{TE} = -\text{KE}$ and $\text{PE} = 2\text{TE} = -2\text{KE}$

(A) $\dfrac{\text{KE}}{\text{TE}} = \dfrac{\text{KE}}{-\text{KE}} = -1$ (Matches III)

(B) $\dfrac{\text{PE}}{\text{KE}} = \dfrac{-2\text{KE}}{\text{KE}} = -2$ (Matches IV)

(C) $\dfrac{\text{PE}}{\text{TE}} = \dfrac{2\text{TE}}{\text{TE}} = 2$ (Matches I)

(D) $\dfrac{\text{KE} + \text{PE}}{\text{TE}} = \dfrac{\text{TE}}{\text{TE}} = 1$ (Matches II)

Thus, the correct matching is (A)-(III), (B)-(IV), (C)-(I), (D)-(II).

Answer: (A)-(III), (B)-(IV), (C)-(I), (D)-(II)