1. Energy of a hydrogen-like species

For a hydrogen-like atom/ion, the energy of the electron in the $n$th orbit is

$E_n = -\frac{13.6\, Z^2}{n^2}\ \text{eV}$

where:

• $Z$ = atomic number
• $n$ = principal quantum number

2. Given condition: $n$ is constant

Since $n$ is fixed, we can write

$E \propto -Z^2$

So the energy varies as the negative of the square of $Z$.

3. Nature of the graph

The equation

$E = -k Z^2 \qquad (k>0)$

represents a parabola opening downward in the sense that:

• for increasing $Z$, $E$ becomes more negative,
• the curve starts near $0$ (from below) when $Z$ is small,
• and falls increasingly rapidly as $Z$ increases.

Thus, the correct $E$ vs $Z$ graph must be a negative quadratic curve lying below the $E=0$ axis.

4. Matching with options

Among the given options, the one corresponding to $E = -\text{constant} \cdot Z^2$ is Option D.

5. Comparison with stored answer

Stored correct answer: D

This matches the derived answer.