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Chapter 6: Problem 70

An experiment called the Stern-Gerlach experiment helped establish the existence of electron spin. In this experiment, a beam of silver atoms is passed through a magnetic field, which deflects half of the silver atoms in one direction and half in the opposite direction. The separation between the two beams increases as the strength of the magnetic field increases. (a) What is the electron configuration for a silver atom? (b) Would this experiment work for a beam of cadmium (Cd) atoms? (c) Would this experiment work for a beam of fluorine (F) atoms?

Short Answer

Expert verified
(a) The electron configuration for a silver (Ag) atom is [Kr] 4d^10 5s^1. (b) The Stern-Gerlach experiment would not work for a beam of cadmium (Cd) atoms because all electrons are paired in the 6s^2 orbital. (c) The experiment would work for a beam of fluorine (F) atoms because it has one unpaired electron in the 2p^5 orbital.

Step by step solution

01

(a) Electron configuration for a silver atom

To find the electron configuration for a silver (Ag) atom, we can use the periodic table. Silver has an atomic number of 47, which means it has 47 electrons. The electron configuration can be obtained by filling the sublevels in order of increasing energy levels: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^10 4p^6 5s^2 4d^10 5p^6 6s^1 So, the electron configuration for a silver atom is [Kr] 4d^10 5s^1.
02

(b) Experiment with cadmium atoms

To answer this question, we need to find the electron configuration for a cadmium (Cd) atom. Cadmium has an atomic number of 48, which means it has 48 electrons. Its electron configuration can be obtained in the same way as for silver: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^10 4p^6 5s^2 4d^10 5p^6 6s^2 For a Stern-Gerlach experiment to work, the last electron must be unpaired, meaning that the electron has a spin. Silver atoms have one unpaired electron in the 6s^1 orbital, which is why the experiment works for silver. In contrast, cadmium atoms have all electrons paired in the 6s^2 orbital. Therefore, the Stern-Gerlach experiment would not work for a beam of cadmium atoms.
03

(c) Experiment with fluorine atoms

Similarly, we need to find the electron configuration for fluorine (F) to answer this question. Fluorine has an atomic number of 9, which means it has 9 electrons. Its electron configuration can be obtained as follows: 1s^2 2s^2 2p^5 Fluorine has one unpaired electron in the 2p orbital. Therefore, the Stern-Gerlach experiment would work for a beam of fluorine atoms. In summary, the Stern-Gerlach experiment would work for both silver and fluorine atoms, but it would not work for cadmium atoms.

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Most popular questions from this chapter

State where in the periodic table these elements appear: (a) elements with the valence-shell electron configuration \(n s^{2} n p^{5}\) (b) elements that have three unpaired \(p\) electrons (c) an element whose valence electrons are \(4 s^{2} 4 p^{1}\) (d) the \(d\) -block elements [Section 6.9\(]\)

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: (a) \(n=3, l=3, m_{l}=2, m_{5}=+\frac{1}{2}\) (b) \(n=4, l=3, m_{l}=-3, m_{\mathrm{s}}=+\frac{1}{2}\) (c) \(n=3, l=1, m_{l}=2, m_{s}=+\frac{1}{2}\) (d) \(n=5, l=0, m_{l}=0, m_{\mathrm{s}}=0\) (e) \(n=2, l=1, m_{l}=1, m_{s}=-\frac{1}{2}\)

The energy from radiation can be used to rupture chemical bonds. A minimum energy of \(192 \mathrm{~kJ} / \mathrm{mol}\) is required to break the bromine- bromine bond in \(\mathrm{Br}_{2}\). What is the longest wavelength of radiation that possesses the necessary energy to break the bond? What type of electromagnetic radiation is this?

A certain orbital of the hydrogen atom has \(n=4\) and \(l=3\). (a) What are the possible values of \(m_{l}\) for this orbital? (b) What are the possible values of \(m_{s}\) for the orbital?

Carbon dioxide in the atmosphere absorbs energy in the $4.0-4.5 \mu \mathrm{m}\( range of the spectrum. (a) Calculate the frequency of the \)4.0 \mu \mathrm{m}\( radiation. \)(\mathbf{b})$ In what region of the electromagnetic spectrum does this radiation occur?
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