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Chapter 7: Problem 63

Determine the maximum number of electrons that can be found in each of the following subshells: \(3 s\), \(3 d, 4 p, 4 f, 5 f\)

Short Answer

Expert verified
The maximum number of electrons in subshells 3s, 3d, 4p, 4f, and 5f are 2, 10, 6, 14, and 14, respectively.

Step by step solution

01

Understanding the Subshell Codes

The subshell code corresponds to the azimuthal or orbital quantum number (l). According to quantum mechanics, the subshell s has l=0, p has l=1, d has l=2, and f has l=3.
02

The number of Orbitals in a Subshell

The number of orbitals in a subshell is determined by the formula \(2l + 1\). So, we can find the number of orbitals for each subshell as follows: 3s (where l=0) has \(2*0+1 = 1\) orbital, 3d (where l=2) has \(2*2+1 = 5\) orbitals, 4p (where l=1) has \(2*1+1 = 3\) orbitals, 4f (where l=3) has \(2*3+1 = 7\) orbitals, and 5f (where l=3) also has \(2*3+1 = 7\) orbitals.
03

Number of Electrons in Each Subshell

Each orbital can hold up to two electrons, as according to the Pauli exclusion principle. Therefore, the number of electrons in a subshell = number of orbitals * 2. Hence, the 3s subshell can have a maximum of 1*2 = 2 electrons, the 3d subshell can have 5*2 = 10 electrons, the 4p subshell can have 3*2 = 6 electrons, the 4f subshell can have 7*2 = 14 electrons, and similarly, the 5f subshell can have a maximum of 7*2 = 14 electrons.

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Most popular questions from this chapter

Indicate which of the following sets of quantum numbers in an atom are unacceptable and explain why: (a) \(\left(1,0, \frac{1}{2}, \frac{1}{2}\right)\) (b) \(\left(3,0,0,+\frac{1}{2}\right)\) (c) \(\left(2,2,1,+\frac{1}{2}\right)\) (d) \(\left(4,3,-2,+\frac{1}{2}\right)\), (e) \((3,2,1,1)\).

What is the difference between a \(2 p_{x}\) and a \(2 p_{y}\) orbital?

What is the wavelength, in \(\mathrm{nm},\) of radiation that has an energy content of \(1.0 \times 10^{3} \mathrm{~kJ} / \mathrm{mol} ?\) In which region of the electromagnetic spectrum is this radiation found?

Is it possible for a fluorescent material to emit radiation in the ultraviolet region after absorbing visible light? Explain your answer.

What is an atomic orbital? How does an atomic orbital differ from an orbit?
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