From the given equation, certain conclusions are drawn: $E = -2.178 \times 10^{-18} \text{ J } \left(\frac{Z^2}{n^2}\right)$. Choose the incorrect statement:

We analyze the statements based on Bohr's theory:

1. Significance of Negative Energy: The negative sign indicates that the electron is bound to the nucleus. An electron at infinite distance ($n=\infty$) has zero energy. A bound electron has lower (negative) energy. (Statement 1 is Correct).
2. Radius Relationship: The radius of a Bohr orbit is given by $r_n \propto n^2$. As $n$ increases, the radius increases. (Statement 2 is Correct).
3. Energy Transitions: The energy difference between two levels is $\Delta E = E_{final} - E_{initial}$. This equation allows the calculation of photon energy during transitions. (Statement 3 is Correct).
4. Binding Energy: For $n=1$, the energy is the most negative (lowest possible potential well). This corresponds to the most stable and tightly bound state. As $n$ increases (e.g., $n=6$), the energy becomes less negative (closer to zero), making the electron less tightly bound. Therefore, saying the electron is "loosely bound" in the smallest orbit ($n=1$) is false. (Statement 4 is Incorrect).