For hydrogen like species, which of the following graphs provides the most appropriate representation of E vs Z plot…

🧠 The $Z^2$ Dependency The energy ($E$) of an electron in a Hydrogen-like atom is determined by the strength of the nucleus ($Z$) and the distance (shell $n$). We need to see how $E$ changes as we vary $Z$ while keeping $n$ constant.

🗺️ The Mathematical Shape

1. The Formula: $E = -k \frac{Z^2}{n^2}$
2. Graphical Logic:
   • $E$ is proportional to $-Z^2$. This is the equation of a parabola opening downwards.
   • For $Z=0$ (no charge), $E=0$ (starts at origin).
   • As $Z$ increases ($1, 2, 3 \dots$), the energy level drops rapidly (becomes more negative).
   • This creates a concave-down curve starting at the origin and heading deeper into the negative energy region.

⚡ The Attraction Rule A bigger nucleus ($Z$) pulls the electron harder. Harder pull means "more bound," and in physics, "more bound" always means a deeper negative potential well. Only a downward-facing curve makes physical sense here.

⚠️ Straight Line Trap If the graph was $E$ vs. $Z^2$, it would be a straight line with a negative slope. Because it's $E$ vs. $Z$, the relationship is quadratic (a parabola), not linear.

$\boxed{\text{Answer: (b)}}$