Chapter 7: Problem 66
Why do the \(3 s, 3 p,\) and \(3 d\) orbitals have the same energy in a hydrogen atom but different energies in a many-electron atom?
/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none}
Learning Materials
Features
Discover
Chapter 7: Problem 66
Why do the \(3 s, 3 p,\) and \(3 d\) orbitals have the same energy in a hydrogen atom but different energies in a many-electron atom?
All the tools & learning materials you need for study success - in one app.
Get started for free
How does de Broglie's hypothesis account for the fact that the energies of the electron in a hydrogen atom are quantized?
Which of the four quantum numbers \(\left(n, \ell, m_{\ell}, m_{s}\right)\) determine (a) the energy of an electron in a hydrogen atom and in a many- electron atom, (b) the size of an orbital, (c) the shape of an orbital, (d) the orientation of an orbital in space?
When an electron makes a transition between energy levels of a hydrogen atom, there are no restrictions on the initial and final values of the principal quantum number \(n\). However, there is a quantum mechanical rule that restricts the initial and final values of the orbital angular momentum \(\ell\). This is the selection rule, which states that \(\Delta \ell=\pm 1,\) that is, in a transition, the value of \(\ell\) can only increase or decrease by one. According to this rule, which of the following transitions are allowed: (a) \(1 s \longrightarrow 2 s\), (b) \(2 p \longrightarrow 1 s\) (c) \(1 s \longrightarrow 3 d\) (d) \(3 d \longrightarrow 4 f\), (e) \(4 d \longrightarrow 3 s ?\)
Thermal neutrons are neutrons that move at speeds comparable to those of air molecules at room temperature. These neutrons are most effective in initiating a nuclear chain reaction among \({ }^{235} \mathrm{U}\) isotopes. Calculate the wavelength (in \(\mathrm{nm}\) ) associated with a beam of neutrons moving at \(7.00 \times 10^{2} \mathrm{~m} / \mathrm{s}\). (Mass of a neutron \(\left.=1.675 \times 10^{-27} \mathrm{~kg} .\right)\)
When copper is bombarded with high-energy electrons, X rays are emitted. Calculate the energy (in joules) associated with the photons if the wavelength of the X rays is \(0.154 \mathrm{nm}\).
What do you think about this solution?
We value your feedback to improve our textbook solutions.