JEE MAIN - Chemistry (2025 - 29th January Evening Shift - No. 14)
For hydrogen like species, which of the following graphs provides the most appropriate representation of E vs Z plot for a constant n?
[E : Energy of the stationary state, Z : atomic number, n = principal quantum number]
_29th_January_Evening_Shift_en_14_1.png)
_29th_January_Evening_Shift_en_14_2.png)
_29th_January_Evening_Shift_en_14_3.png)
_29th_January_Evening_Shift_en_14_4.png)
Explanation
$$E\,vs\,Z\,plot\,(cons\tan t\,n)\left\{ \matrix{ E - Energy\,of\,the\,stationary\,state \hfill \cr Z - atomic\,number \hfill \cr n - \Pr incipal\,quantum\,number \hfill \cr} \right.$$
The formula of energy of hydrogen like species is
$$E = - 13.6{{{z^2}} \over {{n^2}}}eV$$
$$E \propto - {{{z^2}} \over {{n^2}}}$$
For constant n, $$E \propto - {Z^2}$$
Here, E and Z has a quadratic relationship. Since the equation (proportionality) includes a negative sign, the graph of E vs Z will be a downward - opening parabola.
_29th_January_Evening_Shift_en_14_5.png)
The graph is like an upside down U. In the given options, graph 4 is like half upside down parabola.
_29th_January_Evening_Shift_en_14_6.png)
The shape is characteristic of negative quadratic function, where the curve opens downward, with the vertex of the parabola at the origin.
So, the answer is option (4).
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