JEE Main 2025 Apr 4 Shift 1, Chemistry Q20: Dual Character Of Matter And Radiation

JEE Main2025Apr 4, Shift 1Chemistry

Which one of the following about an electron occupying the 1s orbital in a hydrogen atom is incorrect ? (Bohr's radius is represented by $a_{0}$ )

A
The probability density of finding the electron is maximum at the nucleus
B
The electron can be found at a distance $2 a_{0}$ from the nucleus
C
The 1s orbital is spherically symmetrical
D
The total energy of the electron is maximum when it is at a distance $a_{0}$ from the nucleus

Solution

For a 1s electron:

(1) The probability density $∣ ψ ∣^{2}$ for 1s is highest at $r = 0$ (the nucleus). True.

(2) $∣ ψ ∣^{2}$ remains finite at all finite $r$ , so finding the electron at $r = 2 a_{0}$ is allowed. True.

(3) The 1s orbital depends only on $r$ , so it is spherically symmetric. True.

(4) The total energy of an electron bound to a hydrogen atom is a property of the state ( $n = 1$ ), not of the radial position. It does not have a maximum at $r = a_{0}$ ; in fact, the energy is most negative (lowest) for the bound state, and approaches zero (its maximum value) only as $r \to \infty$ . This statement is therefore incorrect.

$∴$ The incorrect statement is option (4).

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JEE Main 2025 Apr 4 Shift 1, Chemistry Q20: Dual Character Of Matter And Radiation

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