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]

JEE Main 2025 (Online) 29th January Evening Shift Chemistry - Structure of Atom Question 11 English Option 1
JEE Main 2025 (Online) 29th January Evening Shift Chemistry - Structure of Atom Question 11 English Option 2
JEE Main 2025 (Online) 29th January Evening Shift Chemistry - Structure of Atom Question 11 English Option 3
JEE Main 2025 (Online) 29th January Evening Shift Chemistry - Structure of Atom Question 11 English Option 4

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.

JEE Main 2025 (Online) 29th January Evening Shift Chemistry - Structure of Atom Question 11 English Explanation 1

The graph is like an upside down U. In the given options, graph 4 is like half upside down parabola.

JEE Main 2025 (Online) 29th January Evening Shift Chemistry - Structure of Atom Question 11 English Explanation 2

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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