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Chapter 7: Problem 99

In the ground state of mercury, Hg, a. how many electrons occupy atomic orbitals with \(n=3 ?\) b. how many electrons occupy \(d\) atomic orbitals? c. how many electrons occupy \(p_{z}\) atomic orbitals? d. how many electrons have spin "up" " \(\left(m_{s}=+\frac{1}{2}\right) ?\)

Short Answer

Expert verified
In the ground state of mercury: a. 18 electrons occupy atomic orbitals with n=3. b. 20 electrons occupy d atomic orbitals. c. 8 electrons occupy \(p_{z}\) atomic orbitals. d. 40 electrons have spin "up" with \(m_{s}=+\frac{1}{2}\).

Step by step solution

01

Identify electron configurations with n=3

We're looking at the electron configuration for mercury and finding the configurations with n=3: \(3s^{2}\) \(3p^{6}\) \(3d^{10}\)
02

Add up the number of electrons

In the n=3 orbitals, we have 2 electrons in 3s, 6 electrons in 3p, and 10 electrons in 3d. So the total number of electrons is 2+6+10 = 18 electrons. b. How many electrons occupy d atomic orbitals?
03

Identify electron configurations with d orbitals

In the electron configuration for mercury, we see 3d and 4d orbitals: \(3d^{10}\) \(4d^{10}\)
04

Add up the number of electrons

There are 10 electrons in 3d orbitals and 10 electrons in 4d orbitals. So the total number of electrons in d atomic orbitals is 10+10 = 20 electrons. c. How many electrons occupy \(p_{z}\) atomic orbitals?
05

Identify electron configurations with p orbitals

In the electron configuration for mercury, we see 2p, 3p, 4p, and 5p orbitals: \(2p^{6}\) \(3p^{6}\) \(4p^{6}\) \(5p^{6}\)
06

Determine the number of electrons in \(p_{z}\) orbitals

Each p subshell has three p orbitals (px, py, and pz), and each orbital can hold a maximum of 2 electrons. Thus, there are 2 electrons in every \(p_{z}\) orbital. Since there are four p orbitals with z-component, there are 2*4 = 8 electrons in \(p_{z}\) atomic orbitals. d. How many electrons have spin "up" with \(m_{s}=+\frac{1}{2}\)?
07

Identify all orbitals

We'll use the electron configuration of mercury to list all the occupied orbitals: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d
08

Determine the number of spin-up electrons in each orbital

Every orbital can house 2 electrons (1 spin up and 1 spin down). Therefore, half of the electrons in each orbital are spin up. Similarly, the other half are spin down.
09

Add up the number of spin-up electrons

Mercury has a total of 80 electrons. Half of them will be spin up. So, there are 80/2 = 40 electrons with spin "up" with \(m_{s}=+\frac{1}{2}\).

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Most popular questions from this chapter

A certain oxygen atom has the electron configuration 1$s^{2} 2 s^{2} 2 p_{x}^{2} 2 p_{y}^{2} .$ How many unpaired electrons are present? Is this an excited state of oxygen? In going from this state to the ground state, would energy be released or absorbed?

An ion having a \(4+\) charge and a mass of 49.9 u has 2 electrons with principal quantum number \(n=1,8\) electrons with \(n=2\) and 10 electrons with \(n=3 .\) Supply as many of the properties for the ion as possible from the information given. (Hint: In forming ions for this species, the 4\(s\) electrons are lost before the 3\(d\) electrons.) a. the atomic number b. total number of \(s\) electrons c. total number of \(p\) electrons d. total number of \(d\) electrons e. the number of neutrons in the nucleus f. the ground-state electron configuration of the neutral atom

The wave function for the 2\(p_{z}\) orbital in the hydrogen atom is $$\psi_{2 p_{z}}=\frac{1}{4 \sqrt{2 \pi}}\left(\frac{Z}{a_{0}}\right)^{3 / 2} \sigma \mathrm{e}^{-\sigma / 2} \cos \theta$$ where \(a_{0}\) is the value for the radius of the first Bohr orbit in meters \(\left(5.29 \times 10^{-11}\right), \sigma\) is \(Z\left(r / a_{0}\right), r\) is the value for the distance from the nucleus in meters, and \(\theta\) is an angle. Calculate the value of \(\psi_{2 p_{z}}^{2}\) at \(r=a_{0}\) for \(\theta=0^{\circ}\left(z \text { axis ) and for } \theta=90^{\circ}\right.\) (xy plane).

How many valence electrons do each of the following elements have, and what are the specific valence electrons for each element? a. Ca b. O c. element 117 d. In e. Ar f. Bi

Are the following statements true for the hydrogen atom only, true for all atoms, or not true for any atoms? a. The principal quantum number completely determines the energy of a given electron. b. The angular momentum quantum number, \(\ell,\) determines the shapes of the atomic orbitals. c. The magnetic quantum number, \(m_{\ell},\) determines the direction that the atomic orbitals point in space.
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