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Chapter 28: Problem 42

What is the maximum possible value of the angular momentum for an outer electron in the ground state of a bromine atom?

Short Answer

Expert verified
Answer: The maximum possible value of the angular momentum for an outer electron in the ground state of a bromine atom is approximately 1.491964608 × 10⁻³⁴ Js.

Step by step solution

01

Find the ground state electron configuration of Bromine

Bromine has an atomic number of 35, meaning it has 35 electrons. The ground state electron configuration can be determined using the periodic table and the aufbau principle. For bromine, it is: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁵
02

Identify the outer electron's quantum numbers

The outer electron is the one with the highest value of the principal quantum number (n). In the case of bromine, the outer electron is in the 4p orbital, which also has the highest energy level. The 4p orbital has the following quantum numbers: n=4, l=1, and ml can vary from -1 to 1.
03

Calculate the maximum possible angular momentum

The maximum possible value of the angular momentum (L) can be calculated using the formula: L = \sqrt{l (l +1)} \hbar Where l is the azimuthal quantum number, and \hbar is the reduced Planck constant (approximately 1.054571817 × 10⁻³⁴ Js). For the outer electron of a bromine atom, the maximum value of l is 1 (given by the 4p orbital).
04

Plug the value of l into the formula and find the maximum angular momentum

Now we can plug the maximum value of l (1) into the formula for angular momentum: L = \sqrt{1(1 + 1)} \hbar L = \sqrt{2} \hbar Thus, the maximum possible value of the angular momentum of the outer electron in the ground state of a bromine atom is sqrt(2) times the reduced Planck constant, which is approximately 1.491964608 × 10⁻³⁴ Js.

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Most popular questions from this chapter

How many electron states of the H atom have the quantum numbers \(n=3\) and \(\ell=1 ?\) Identify each state by listing its quantum numbers.
What is the ground-state electron configuration of nickel (Ni, atomic number 28 )?
The distance between atoms in a crystal of \(\mathrm{NaCl}\) is $0.28 \mathrm{nm} .$ The crystal is being studied in a neutron diffraction experiment. At what speed must the neutrons be moving so that their de Broglie wavelength is \(0.28 \mathrm{nm} ?\)
(a) Find the magnitude of the angular momentum \(\overrightarrow{\mathbf{L}}\) for an electron with \(n=2\) and \(\ell=1\) in terms of \(\hbar .\) (b) What are the allowed values for \(L_{2} ?\) (c) What are the angles between the positive z-axis and \(\overline{\mathbf{L}}\) so that the quantized components, \(L_{z},\) have allowed values?
In the Davisson-Germer experiment (Section \(28.2),\) the electrons were accelerated through a \(54.0-\mathrm{V}\) potential difference before striking the target. (a) Find the de Broglie wavelength of the electrons. (b) Bragg plane spacings for nickel were known at the time; they had been determined through x-ray diffraction studies. The largest plane spacing (which gives the largest intensity diffraction maxima) in nickel is \(0.091 \mathrm{nm} .\) Using Bragg's law [Eq. ( \(25-15\) )], find the Bragg angle for the first-order maximum using the de Broglie wavelength of the electrons. (c) Does this agree with the observed maximum at a scattering angle of \(130^{\circ} ?\) [Hint: The scattering angle and the Bragg angle are not the same. Make a sketch to show the relationship between the two angles.]
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