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Chapter 6: Problem 54

Give the values for \(n, l\), and \(m_{l}\) for (a) each orbital in the \(2 p\) subshell, (b) each orbital in the \(5 d\) subshell.

Short Answer

Expert verified
(a) For each orbital in the \(2p\) subshell, the quantum numbers are: - Orbital 1: \(n=2, l=1, m_l=-1\) - Orbital 2: \(n=2, l=1, m_l=0\) - Orbital 3: \(n=2, l=1, m_l=1\) (b) For each orbital in the \(5d\) subshell, the quantum numbers are: - Orbital 1: \(n=5, l=2, m_l=-2\) - Orbital 2: \(n=5, l=2, m_l=-1\) - Orbital 3: \(n=5, l=2, m_l=0\) - Orbital 4: \(n=5, l=2, m_l=1\) - Orbital 5: \(n=5, l=2, m_l=2\)

Step by step solution

01

Principal Quantum Number n

For the \(2p\) subshell, the principal quantum number, \(n = 2\).
02

Azimuthal Quantum Number l

In the \(2p\) subshell ("p" subshell), the azimuthal quantum number, \(l = 1\).
03

Magnetic Quantum Number m_l

For the p orbital (\(l=1\)), the magnetic quantum number, \(m_l\), can have values of -1, 0, and 1. So, the orbital quantum numbers for the \(2p\) subshell are: - Orbital 1: \(n=2, l=1, m_l=-1\) - Orbital 2: \(n=2, l=1, m_l=0\) - Orbital 3: \(n=2, l=1, m_l=1\) (b) Each orbital in the \(5d\) subshell:
04

Principal Quantum Number n

For the \(5d\) subshell, the principal quantum number, \(n = 5\).
05

Azimuthal Quantum Number l

In the \(5d\) subshell ("d" subshell), the azimuthal quantum number, \(l = 2\).
06

Magnetic Quantum Number m_l

For the d orbital (\(l=2\)), the magnetic quantum number, \(m_l\), can have values of -2, -1, 0, 1, and 2. So, the orbital quantum numbers for the \(5d\) subshell are: - Orbital 1: \(n=5, l=2, m_l=-2\) - Orbital 2: \(n=5, l=2, m_l=-1\) - Orbital 3: \(n=5, l=2, m_l=0\) - Orbital 4: \(n=5, l=2, m_l=1\) - Orbital 5: \(n=5, l=2, m_l=2\)

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Most popular questions from this chapter

The Lyman series of emission lines of the hydrogen atom are those for which \(n_{f}=1 .\) (a) Determine the region of the electromagnetic spectrum in which the lines of the Lyman series are observed. (b) Calculate the wavelengths of the first three lines in the Lyman series- those for which \(n_{i}=2,3,\) and 4 .

Microwave ovens use microwave radiation to heat food. The energy of the microwaves is absorbed by water molecules in food and then transferred to other components of the food. (a) Suppose that the microwave radiation has a wavelength of \(11.2 \mathrm{~cm} .\) How many photons are required to heat \(200 \mathrm{~mL}\) of coffee from \(23^{\circ} \mathrm{C}\) to \(60^{\circ} \mathrm{C} ?\) (b) Suppose the microwave's power is \(900 \mathrm{~W}\) ( 1 Watt \(=1\) joule-second). How long would you have to heat the coffee in part (a)?

Using the periodic table as a guide, write the condensed electron configuration and determine the number of unpaired electrons for the ground state of (a) \(\mathrm{Si},\) (b) \(\mathrm{Zn}\), (c) \(\mathrm{Zr},(\mathrm{d}) \mathrm{Sn}\) (e) \(\mathrm{Ba},(\mathrm{f}) \mathrm{Tl}\)

Bohr's model can be used for hydrogen-like ions -ions that have only one electron, such as \(\mathrm{He}^{+}\) and \(\mathrm{Li}^{2+}\). (a) Why is the Bohr model applicable to \(\mathrm{He}^{+}\) ions but not to neutral He atoms? (b) The ground-state energies of \(\mathrm{H}, \mathrm{He}^{+},\) and \(\mathrm{Li}^{2+}\) are tabulated as follows: By examining these numbers, propose a relationship between the ground-state energy of hydrogen-like systems and the nuclear charge, \(Z\). (c) Use the relationship you derive in part (b) to predict the ground-state energy of the \(\mathrm{C}^{5+}\) ion.

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