The energy of the electron in any given state for the hydrogen atom is $-13.6/n^2\, eV$. Identify the correct statements among the following.

(A) the negative sign in $-13.6\, eV$ signifies that the electron is bound to the nucleus.
(B) the negative sign in $-13.6\, eV$ signifies that the electron requires $13.6\, eV$ energy to be separated from the nucleus.
(C) $3.4\, eV$ energy is required to take the electron from the ground to the first excited state.
(D) to find the energy of third excited state, the value of $n$ is 4.

Choose the correct answer from the options given below:

(A), (B) and (D) only

The correct answer is Option (1) → (A), (B) and (D) only

(A) the negative sign in $-13.6\, eV$ signifies that the electron is bound to the nucleus. (Correct)
(B) the negative sign in $-13.6\, eV$ signifies that the electron requires $13.6\, eV$ energy to be separated from the nucleus. (Correct)
(C) $3.4\, eV$ energy is required to take the electron from the ground to the first excited state. (Incorrect)
(D) to find the energy of third excited state, the value of $n$ is 4. (Correct)