JEE Chemistry 2025 Question with Solution

Given: Statements about an electron in the $1s$ orbital of a hydrogen atom are given.

Find: The incorrect statement.

The solution evaluates each statement using properties of the hydrogen atom.

1. The probability density of finding the electron is maximum at the nucleus. For the $1s$ orbital, the wave function is greatest at the nucleus, so this statement is correct.

2. The electron can be found at a distance $2 \mathrm{a}_{0}$ from the nucleus. Quantum mechanically, there is non-zero probability of finding the electron at distances other than zero, including $2 \mathrm{a}_{0}$, so this statement is correct.

3. The $1s$ orbital is spherically symmetrical. Its probability distribution depends only on distance from the nucleus, not direction, so this statement is correct.

4. The total energy of the electron is maximum when it is at a distance $\mathrm{a}_{0}$ from the nucleus. This is incorrect because for a given energy level, the total energy is quantized and does not depend on the electron's position within the orbital.

Therefore, the incorrect statement is option D.

Given: An electron occupies the $1s$ orbital in a hydrogen atom.

Find: Which statement is incorrect.

The key ideas mentioned in the solution are probability density, allowed distance from the nucleus, spherical symmetry, and total energy.

• Probability density: The probability density is maximum at the nucleus for the $1s$ orbital. So statement A is correct.
• Distance from nucleus: The electron may be found at $2 \mathrm{a}_{0}$ because the probability at such a distance is not zero. So statement B is correct.
• Symmetry: The $1s$ orbital is spherically symmetrical. So statement C is correct.
• Total energy: The total energy for the electron in the $1s$ state is fixed for that state and is not maximum specifically at $\mathrm{a}_{0}$. So statement D is incorrect.

Hence, the correct option is D.