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

This problem concerns the characteristics of the hydrogen atom's electron in a 1s orbital. Let's analyze each statement:

1. The probability density of finding the electron is highest at the nucleus: The wave function for a 1s orbital electron exhibits spherical symmetry and is maximal at the nucleus. This statement is accurate.
2. The electron may be detected at a distance of \(2\mathrm{a}_{0}\) from the nucleus: Quantum mechanics dictates a non-zero probability of locating the electron at various distances \(r\) from the nucleus, including \(2\mathrm{a}_{0}\). This statement is plausible.
3. The 1s orbital possesses spherical symmetry: The 1s orbital is indeed spherically symmetrical, as its probability distribution is solely dependent on the radial distance from the nucleus, not the angular orientation. This statement is accurate.
4. The electron's total energy is maximal at a distance of \(\mathrm{a}_{0}\) from the nucleus: According to the Bohr model, the total energy of a 1s orbital electron is constant and independent of its position relative to the nucleus, aside from its quantized energy level. Consequently, this statement is erroneous.

The assertion "The total energy of the electron is maximum when it is at a distance \(\mathrm{a}_{0}\) from the nucleus" is incorrect because the electron's energy in an orbit is determined by its energy level, not its precise location within an orbital. Energy is quantized and invariant 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.