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Chapter 6: Problem 71

What is the maximum number of electrons that can occupy each of the following subshells? (a) 3p, (b) \(5 d,(\mathbf{c}) 2 s,(\mathbf{d}) 4 f .\)

Short Answer

Expert verified
The maximum number of electrons that can occupy the given subshells are: (a) 3p: \(6\) electrons, (b) 5d: \(10\) electrons, (c) 2s: \(2\) electrons, and (d) 4f: \(14\) electrons.

Step by step solution

01

Determine the angular quantum number (鈩�) for each subshell

For each subshell given, determine the angular quantum number (鈩�) corresponding to the subshell type (s=0, p=1, d=2, f=3): (a) 3p - 鈩�=1 (p subshell) (b) 5d - 鈩�=2 (d subshell) (c) 2s - 鈩�=0 (s subshell) (d) 4f - 鈩�=3 (f subshell)
02

Apply the 2(2鈩� + 1) formula for each subshell

Now that we have the angular quantum numbers for each subshell, we will use the formula 2(2鈩�+1) to find the maximum number of electrons that can occupy each given subshell. (a) For 3p: Maximum number of electrons = 2(2(1) + 1) = 2(2+1) = 2(3) = 6 (b) For 5d: Maximum number of electrons = 2(2(2) + 1) = 2(4+1) = 2(5) = 10 (c) For 2s: Maximum number of electrons = 2(2(0) + 1) = 2(0+1) = 2(1) = 2 (d) For 4f: Maximum number of electrons = 2(2(3) + 1) = 2(6+1) = 2(7) = 14
03

Write the final answer

The maximum number of electrons that can occupy each of the given subshells are: (a) 3p: 6 electrons (b) 5d: 10 electrons (c) 2s: 2 electrons (d) 4f: 14 electrons

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Quantum Numbers
Quantum numbers are like an address system for electrons within an atom, helping us understand their position and energy. There are four quantum numbers, but we'll focus on the angular quantum number for now.
  • The **principal quantum number (n)**: This indicates the main energy level or shell. For example, in 3p, the principal quantum number is 3.
  • The **angular (or azimuthal) quantum number (鈩�)**: This determines the shape of the orbital. It's key to understanding what type of subshell we have, whether it鈥檚 s, p, d, or f. The angular quantum number can be 0 (s), 1 (p), 2 (d), or 3 (f).
  • Other quantum numbers can specify orientations and spins, but let's keep it simple for now.
These numbers together help predict where electrons are and how many fit into certain areas around an atom. They play a crucial role in determining the chemical behavior of elements.
Subshell
A subshell is a subdivision of electron shells separated by electron orbitals. It provides a more detailed structure than the principal energy level alone.
  • Each shell can have one or more subshells, identified by the value of the angular quantum number (鈩�).
  • Subshells are usually labeled s, p, d, and f, corresponding to the values of 鈩�: 0, 1, 2, and 3, respectively.
  • For instance, in the 3p subshell, 'p' indicates the shape and type of the orbitals, while 3 is the main energy level.
Subshells are crucial in predicting electron arrangements and calculating how many electrons can fit, using specific formulas based on quantum numbers. Methods like the 2(2鈩� + 1) formula help determine these capacities by calculating possible orientations.
Angular Quantum Number
The angular quantum number (鈩�) plays a vital role in determining the shape and type of an electron's orbital. It helps us visualize what the space around an atom looks like where electrons might be found.
  • This number varies based on the type of subshell:
    • s (鈩�=0),
    • p (鈩�=1),
    • d (鈩�=2),
    • f (鈩�=3).
  • Recognizing the angular quantum number allows us to use the formula for maximum electron capacity in a subshell: 2(2鈩� + 1).
  • Applying these values shows us potential numbers like in a 2s subshell (鈩�=0) fitting 2 electrons, or a 4f subshell (鈩�=3) accommodating 14 electrons.
Understanding the angular quantum number enables us to map out where electrons are likely to be and how atoms interact, impacting everything from chemical reactions to the properties of substances.

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Most popular questions from this chapter

If human height were quantized in 1 -foot increments, what would happen to the height of a child as she grows up: (i) The child's height would never change, (ii) the child's height would continuously get greater, (iii) the child's height would increase in "jumps" of 1 foot at a time, or (iv) the child's height would increase in jumps of 6 inches?

What is the maximum number of electrons in an atom that can have the following quantum numbers? (a) \(n=3, m_{l}=-2 ;(\mathbf{b}) n=4, l=3 ;(\mathbf{c}) n=5, l=3, m_{l}=2\) (d) \(n=4, l=1, m_{l}=0\)

Neutron diffraction is an important technique for determining the structures of molecules. Calculate the velocity of a neutron needed to achieve a wavelength of 1.25 A. (Refer to the inside cover for the mass of the neutron.)

The Lyman series of emission lines of the hydrogen atom are those for which \(n_{1}=1 .\) (a) Determine the region of the electromagnetic spectrum in which the lines of the Lyman series are observed. (b) Calculate the wavelengths of the first three lines in the Lyman series - those for which \(n_{1}=2,3,\) and \(4 .\)

The discovery of hafnium, element number \(72,\) provided a controversial episode in chemistry. G. Urbain, a French chemist, claimed in 1911 to have isolated an element number 72 from a sample of rare earth (elements \(58-71 )\) compounds. However, Niels Bohr believed that hafnium was more likely to be found along with zirconium than with the rare earths. D. Coster and G. von Hevesy, working in Bohr's laboratory in Copenhagen, showed in 1922 that element 72 was present in a sample of Norwegian zircon, an ore of zirconium. (The name hafnum comes from the Latin name for Copenhagen, Hafnia).(a) How would you use electron configuration arguments to justify Bohr's prediction? (b) Zirconium, hafnium's neighbor in group 4 \(\mathrm{B}\) , can be produced as a metal by reduction of solid \(\mathrm{ZrCl}_{4}\) with molten sodium metal. Write a balanced chemical equation for the reaction. Is this an oxidation- reduction reaction? If yes, what is reduced and what is oxidized? (c) Solid zirconium dioxide, \(\mathrm{ZrO}_{2},\) reacts with chlorine gas in the presence of carbon. The products of the reaction are \(Z r \mathrm{Cl}_{4}\) and two gases, \(\mathrm{CO}_{2}\) and \(\mathrm{CO}\) in the ratio \(1 : 2 .\) Write a balanced chemical equation for the reaction. Starting with a \(55.4-\mathrm{g}\) sample of \(\mathrm{ZrO}_{2},\) calculate the mass of \(\mathrm{ZrCl}_{4}\) formed, assuming that \(Z r O_{2}\) is the limiting reagent and assuming 100\(\%\) yield. (d) Using their electron configurations, account for the fact that \(\mathrm{Zr}\) and \(\mathrm{Hf}\) form chlorides \(\mathrm{MCl}_{4}\) and oxides \(\mathrm{MO}_{2}\)
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