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Chapter 8: Problem 122

Describe two ways in which the orbitals of multielectron atoms resemble hydrogen orbitals and two ways in which they differ from hydrogen orbitals.

Short Answer

Expert verified
Hydrogen and multi-electron atomic orbitals resemble each other in terms of shapes and allowed quantum numbers. They differ in terms of energy levels and the existence of the 'shielding' effect.

Step by step solution

01

Understanding Atomic Orbitals

Atomic orbitals are regions in an atom where the probability of finding an electron is high. Each of these orbitals has a certain energy level and shape associated with it. They help in understanding the behavior of electrons in an atom.
02

Similarities between Multi-electron and Hydrogen Orbitals

1. Shapes and Number: Both hydrogen and multi-electron atomic orbitals have the similar shapes and the same number of orbitals in each energy level. For example, there is one s orbital, three p orbitals and five d orbitals regardless of the atom. 2. Quantum Numbers: For both types of atoms, the allowed quantum numbers for the orbitals are the same. There are four types of quantum numbers, including principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (m), and spin quantum number (s). The values these can take are the same for hydrogen as for multi-electron atoms.
03

Differences between Multi-electron and Hydrogen Orbitals

1. Energy Levels: In a hydrogen atom, the energy of an orbital depends solely on the principal quantum number (n) i.e., orbitals on the same energy level (n) have the same energy. However, in multi-electron atoms, the energy of an orbital also depends on the azimuthal quantum number (l). That is, energy increases with increasing l for a given n. 2. Shielding: Shielding refers to the blocking of the attractive forces from the nuclear protons by other electrons. This occurs in multi-electron atoms but not in the hydrogen atom as it has only one electron and no electron-electron interactions take place.

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Most popular questions from this chapter

Between which two orbits of the Bohr hydrogen atom must an electron fall to produce light of wavelength \(1876 \mathrm{nm} ?\)

Without doing detailed calculations, indicate which of the following electron transitions in the hydrogen atom results in the emission of light of the longest wavelength. (a) \(n=4\) to \(n=3 ;\) (b) \(n=1\) to \(n=2\) (c) \(n=1\) to \(n=6 ;\) (d) \(n=3\) to \(n=2\).

When atoms in excited states collide with unexcited atoms they can transfer their excitation energy to those atoms. The most efficient energy transfer occurs when the excitation energy matches the energy of an excited state in the unexcited atom. Assuming that we have a collection of excited hydrogen atoms in the \(2 s^{1}\) excited state, are there any transitions of \(\mathrm{He}^{+}\) that could be most efficiently excited by the hydrogen atoms?

Calculate the wavelength of the electromagnetic radiation required to excite a proton from the ground state to the level with \(n=4\) in a one-dimensional box 50. pm long.

The following electron configurations correspond to the ground states of certain elements. Name each element. (a) \([\mathrm{Ar}] 3 d^{10} 4 s^{2} 4 p^{3} ;\) (b) \([\mathrm{Ne}] 3 s^{2} 3 p^{4} ;\) (c) \([\mathrm{Ar}] 3 d^{1} 4 s^{2}\) (d) \([\mathrm{Kr}] 4 d^{6} 5 s^{2} ;\) (e) \([\mathrm{Xe}] 4 f^{12} 6 s^{2}\)
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