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Chapter 6: Problem 57

Give the numerical values of \(n\) and \(l\) corresponding to each of the following orbital designations: (a) \(3 p,(\mathbf{b}) 2 s,(\mathbf{c}) 4 f,(\mathbf{d}) 5 d\)

Short Answer

Expert verified
For the given orbital designations, the numerical values of n and l are as follows: (a) 3p orbital: n = 3 and l = 1. (b) 2s orbital: n = 2 and l = 0. (c) 4f orbital: n = 4 and l = 3. (d) 5d orbital: n = 5 and l = 2.

Step by step solution

01

(a) 3p orbital

For the 3p orbital, the principal quantum number is already provided, which is n = 3. The letter "p" corresponds to the azimuthal quantum number value l = 1. Thus, for a 3p orbital, n = 3 and l = 1.
02

(b) 2s orbital

For the 2s orbital, the principal quantum number is given as n = 2. The letter "s" corresponds to the azimuthal quantum number value l = 0. Thus, for a 2s orbital, n = 2 and l = 0.
03

(c) 4f orbital

For the 4f orbital, the principal quantum number is given as n = 4. The letter "f" corresponds to the azimuthal quantum number value l = 3. Thus, for a 4f orbital, n = 4 and l = 3.
04

(d) 5d orbital

For the 5d orbital, the principal quantum number is given as n = 5. The letter "d" corresponds to the azimuthal quantum number value l = 2. Thus, for a 5d orbital, n = 5 and l = 2.

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Most popular questions from this chapter

Determine whether each of the following sets of quantum numbers for the hydrogen atom are valid. If a set is not valid, indicate which of the quantum numbers has a value that is not valid: $$ \begin{array}{l}{\text { (a) } n=4, l=1, m_{l}=2, m_{s}=-\frac{1}{2}} \\\ {\text { (b) } n=4, l=3, m_{l}=-3, m_{s}=+\frac{1}{2}}\\\\{\text { (c) } n=3, l=2, m_{l}=-1, m_{s}=+\frac{1}{2}} \\ {\text { (d) } n=5, l=0, m_{l}=0, m_{s}=0} \\ {\text { (e) } n=2, l=2, m_{l}=1, m_{s}=+\frac{1}{2}}\end{array} $$

The energy from radiation can be used to cause the rupture of chemical bonds. A minimum energy of 242 \(\mathrm{kJ} / \mathrm{mol}\) is required to break the chlorine-chlorine bond in \(\mathrm{Cl}_{2} .\) What is the longest wavelength of radiation that possesses the necessary energy to break the bond? What type of electromagnetic radiation is this?

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In the experiment shown schematically below, a beam of neutral atoms is passed through a magnetic field. Atoms that have unpaired electrons are deflected in different directions in the magnetic field depending on the value of the electron spin quantum number. In the experiment illustrated, we envision that a beam of hydrogen atoms splits into two beams. (a) What is the significance of the observation that the single beam splits into two beams? (b) What do you think would happen if the strength of the magnet were increased? (c) What do you think would happen if the beam of hydrogen atoms were replaced with a beam of helium atoms? Why? (d) The relevant experiment was first performed by Otto Stern and Walter Gerlach in \(1921 .\) They used a beam of Ag atoms in the experiment. By considering the electron configuration of a silver atom, explain why the single beam splits into two beams.
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