JEE Main · 2025 · 29 Jan 2025 · Shift 2 · Atomic Structure

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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]

(A)(see structure)
(B)(see structure)
✓ Correct
(C)(see structure)
(D)(see structure)

Answer: (B)

Solution

For a hydrogen-like species,

E_{n} = - \frac{13.6 Z ^{2}}{n ^{2}}

eV. At fixed

n

, this reduces to

E = - k Z^{2}

with

k = 13.6/ n^{2} > 0

, a downward-opening parabola in

Z

that passes through the origin at

Z = 0

and becomes increasingly negative as

Z

increases. The graph must start at

E = 0

for

Z = 0

and curve smoothly downward into negative

E

, with the magnitude of the slope growing as

Z

grows — the shape traced in option B.

JEE Main · 2025 · 29 Jan 2025 · Shift 2 · Single correct option

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