Question

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

• A. The probability density of finding the electron is maximum at the nucleus
• B. The electron can be found at a distance $2 \mathrm{a}_{0}$ 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 $\mathrm{a}_{0}$ from the nucleus

Hint:

The probability density, distance from the nucleus, spherical symmetry, and total energy of an electron in the 1s orbital are important properties to consider.

Answer 1

The Correct Option is D

The problem pertains to the properties of the hydrogen atom's electron in a 1s orbital. Let's evaluate each option:

1. The probability density of finding the electron is maximum at the nucleus: The wave function for an electron in the 1s orbital is spherically symmetrical and greatest at the nucleus. This statement is correct.
2. The electron can be found at a distance \(2\mathrm{a}_{0}\) from the nucleus: According to quantum mechanics, there is a non-zero probability of finding the electron at distances \(r\) that are different from zero, including \(2\mathrm{a}_{0}\). This statement is plausible.
3. The 1s orbital is spherically symmetrical: The 1s orbital indeed has spherical symmetry as its probability distribution depends only on the distance from the nucleus, not on the direction. 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: In the Bohr model, the total energy of the electron in the 1s orbital is constant and does not depend on its position relative to the nucleus beyond quantized energy levels. Hence, this statement is incorrect.

The statement "The total energy of the electron is maximum when it is at a distance \(\mathrm{a}_{0}\) from the nucleus" is incorrect because the energy of the electron in its orbit depends on its energy level, not its specific location within an orbital. The energy is quantized and constant for a given level.

Therefore, the correct answer is: The total energy of the electron is maximum when it is at a distance \(\mathrm{a}_{0}\) from the nucleus.

Answer 2

1. Probability density: - The probability density of finding the electron is maximum at the nucleus. 
2. Distance from the nucleus: - The electron can be found at a distance $2 \mathrm{a}_{0}$ from the nucleus. 
3. Spherical symmetry: - The 1s orbital is spherically symmetrical. 
4. Total energy: - The total energy of the electron is maximum when it is at a distance $\mathrm{a}_{0}$ from the nucleus. 
This statement is incorrect. Therefore, the correct answer is (4).