Which of the following statements is incorrect?. (a) The...

Name: Problem 134, Chapter 2: Problems in Physical Chemistry for JEE
Uploaded: 2021-08-11T15:04:34-08:00
Duration: 1 min 21 s
Channel: Ajay Singhal
Description: Which of the following statements is incorrect?. (a) The concepts of "penetration" and "shielding" are important in deciding the energetic ordering of orbitals in multi-electron atoms (b) A wave-function can have positive and negative values (c) "Radial nodes" can appear in radial probability distribution functions (d) The absolute size of an orbital is given by the principal quantum number.

Which of the following statements is incorrect?. (a) The concepts of "penetration" and "shielding" are important in deciding the energetic ordering of orbitals in multi-electron atoms (b) A wave-function can have positive and negative values (c) "Radial nodes" can appear in radial probability distribution functions (d) The absolute size of an orbital is given by the principal quantum number.

Which of the following statements is incorrect?.
(a) The concepts of "penetration" and "shielding" are important in deciding the energetic ordering of orbitals in multi-electron atoms
(b) A wave-function can have positive and negative values
(c) "Radial nodes" can appear in radial probability distribution functions
(d) The absolute size of an orbital is given by the principal quantum number.

Key Concepts

Principal Quantum Number and Orbital Size

The principal quantum number largely determines the energy level and average distance of an electron from the nucleus, but it does not strictly define the absolute size of an orbital. Instead, the size is influenced by the overall shape of the orbital, including factors like penetration and the number of nodes in the wavefunction.

Radial Nodes

Radial nodes are specific points (or distances from the nucleus) where the radial part of the wavefunction becomes zero, leading to zero probability density at those points. These nodes are an intrinsic feature of the solutions to the radial Schrödinger equation and play an important role in determining the distribution of electron density.

Penetration and Shielding

In multi-electron atoms, penetration refers to the extent to which an electron's orbital extends into the high nuclear-charge region near the nucleus, while shielding refers to the reduction in nuclear attraction felt by an electron due to the presence of other electrons. These concepts explain why orbitals with the same principal quantum number but different angular momentum can have different energy levels.

Wavefunction Characteristics

A wavefunction in quantum mechanics can take on both positive and negative values and is a complex mathematical function representing the state of a particle. Although the wavefunction itself is not directly observable, its square modulus yields the probability density, which must be non-negative.

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