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Chapter 2: Problem 98

Give a possible set of values of the four quantum numbers for the \(4 s\) and \(3 d\) electrons in titanium.

Short Answer

Expert verified
For the 4s electrons in titanium, the possible sets of quantum numbers are (n = 4, l = 0, m_l = 0, m_s = +1/2) and (n = 4, l = 0, m_l = 0, m_s = -1/2). For the 3d electrons, the possible sets of quantum numbers are: n = 3, l = 2, and m_l ranges from -2 to 2 with m_s being either +1/2 or -1/2, yielding ten possible sets of values in total.

Step by step solution

01

Identify the electronic configuration

To determine the set of quantum numbers for the 4s and 3d electrons, we first need to find the electronic configuration of titanium. Titanium (Ti) has an atomic number of 22. Therefore, it has 22 electrons. The electronic configuration for titanium is: 1s虏 2s虏 2p鈦� 3s虏 3p鈦� 4s虏 3d虏 Now, we'll focus on the 4s and 3d electrons.
02

Determine the principal quantum number (n)

The principal quantum number (n) is directly related to the energy level of the electron. In this case, the 4s electrons have n = 4, while the 3d electrons have n = 3.
03

Determine the azimuthal quantum number (l)

The azimuthal quantum number (l) is related to the shape of the orbital. The values for l depend on the value of n and range from 0 to (n-1). Here, we already know the orbitals: s and d. The s orbital corresponds to l = 0, and the d orbital corresponds to l = 2. So for 4s electrons, l = 0, and for 3d electrons, l = 2.
04

Determine the magnetic quantum number (m_l)

The magnetic quantum number (m_l) describes the orientation of the orbital. The values for m_l depend on the value of l and range from -l to +l, including 0. For 4s electrons (l = 0), there is only one possible value for m_l: 0. For 3d electrons (l = 2), there are five possible values for m_l: -2, -1, 0, 1, and 2.
05

Determine the spin quantum number (m_s)

The spin quantum number (m_s) describes the intrinsic angular momentum of the electron. There are two possible values for m_s: +1/2 and -1/2, representing spin-up and spin-down electrons, respectively.
06

Find the possible sets of quantum numbers

Now, we can combine the information to find the possible sets of quantum numbers for the 4s and 3d electrons in titanium. For 4s electrons: 1. n = 4, l = 0, m_l = 0, m_s = +1/2 2. n = 4, l = 0, m_l = 0, m_s = -1/2 For 3d electrons: 1. n = 3, l = 2, m_l = -2, m_s = +1/2 2. n = 3, l = 2, m_l = -2, m_s = -1/2 3. n = 3, l = 2, m_l = -1, m_s = +1/2 4. n = 3, l = 2, m_l = -1, m_s = -1/2 5. n = 3, l = 2, m_l = 0, m_s = +1/2 6. n = 3, l = 2, m_l = 0, m_s = -1/2 7. n = 3, l = 2, m_l = 1, m_s = +1/2 8. n = 3, l = 2, m_l = 1, m_s = -1/2 9. n = 3, l = 2, m_l = 2, m_s = +1/2 10. n = 3, l = 2, m_l = 2, m_s = -1/2 These are the possible sets of values for the four quantum numbers for the 4s and 3d electrons in titanium.

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Most popular questions from this chapter

As the weapons officer aboard the Starship Chemistry, it is your duty to configure a photon torpedo to remove an electron from the outer hull of an enemy vessel. You know that the work function (the binding energy of the electron) of the hull of the enemy ship is \(7.52 \times 10^{-19} \mathrm{J}\) a. What wavelength does your photon torpedo need to be to eject an electron? b. You find an extra photon torpedo with a wavelength of \(259 \mathrm{nm}\) and fire it at the enemy vessel. Does this photon torpedo do any damage to the ship (does it eject an electron)? c. If the hull of the enemy vessel is made of the element with an electron configuration of \([\mathrm{Ar}] 4 s^{1} 3 d^{10},\) what metal is this?

Answer the following questions, assuming that \(m_{s}\) could have three values rather than two and that the rules for \(n, \ell,\) and \(m_{\ell}\) are the normal ones. a. How many electrons would an orbital be able to hold? b. How many elements would the first and second periods in the periodic table contain? c. How many elements would be contained in the first transition metal series? d. How many electrons would the set of \(4 f\) orbitals be able to hold?

Element 106 has been named seaborgium, \(\mathrm{Sg}\), in honor of Glenn Seaborg, discoverer of the first transuranium element. a. Write the expected electron configuration for element 106 b. What other element would be most like element 106 in its properties?

Assume that a hydrogen atom's electron has been excited to the \(n=5\) level. How many different wavelengths of light can be emitted as this excited atom loses energy?

Carbon absorbs energy at a wavelength of \(150 . \mathrm{nm.}\) The total amount of energy emitted by a carbon sample is \(1.98 \times 10^{5} \mathrm{J}\) Calculate the number of carbon atoms present in the sample, assuming that each atom emits one photon.
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