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Chapter 6: Problem 65

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

Short Answer

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

Step by step solution

01

Identify the quantum numbers

For a 3p subshell, the principle quantum number (n) is 3 and the angular momentum quantum number (l) is 1 (since p corresponds to l=1).
02

Calculate the maximum number of electrons

Using the formula 2(2l+1), we can calculate the number of electrons in the 3p subshell: \(2(2(1)+1)=2(3)=6\) Ultimately, the 3p subshell can hold a maximum of 6 electrons. #b) 5d Subshell Maximum Electrons#
03

Identify the quantum numbers

For a 5d subshell, the principle quantum number (n) is 5 and the angular momentum quantum number (l) is 2 (since d corresponds to l=2).
04

Calculate the maximum number of electrons

Using the formula 2(2l+1), we can calculate the number of electrons in the 5d subshell: \(2(2(2)+1)=2(5)=10\) Ultimately, the 5d subshell can hold a maximum of 10 electrons. #c) 2s Subshell Maximum Electrons#
05

Identify the quantum numbers

For a 2s subshell, the principle quantum number (n) is 2 and the angular momentum quantum number (l) is 0 (since s corresponds to l=0).
06

Calculate the maximum number of electrons

Using the formula 2(2l+1), we can calculate the number of electrons in the 2s subshell: \(2(2(0)+1)=2(1)=2\) Ultimately, the 2s subshell can hold a maximum of 2 electrons. #d) 4f Subshell Maximum Electrons#
07

Identify the quantum numbers

For a 4f subshell, the principle quantum number (n) is 4 and the angular momentum quantum number (l) is 3 (since f corresponds to l=3).
08

Calculate the maximum number of electrons

Using the formula 2(2l+1), we can calculate the number of electrons in the 4f subshell: \(2(2(3)+1)=2(7)=14\) Ultimately, the 4f subshell can hold a maximum of 14 electrons.

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Most popular questions from this chapter

The rays of the Sun that cause tanning and burning are in the ultraviolet portion of the electromagnetic spectrum. These rays are categorized by wavelength. So-called UV-A radiation has wavelengths in the range of \(320-380 \mathrm{nm},\) whereas \(\mathrm{UV}-\mathrm{B}\) radiation has wavelengths in the range of \(290-320 \mathrm{nm}\). (a) Calculate the frequency of light that has a wavelength of \(320 \mathrm{nm}\). (b) Calculate the energy of a mole of 320 -nm photons. (c) Which are more energetic, photons of UV-A radiation or photons of UV-B radiation? (d) The UV-B radiation from the Sun is considered a greater cause of sunburn in humans than is UV-A radiation. Is this observation consistent with your answer to part \((c)\) ?

Sodium metal requires a photon with a minimum energy of \(4.41 \times 10^{-19} \mathrm{~J}\) to emit electrons. (a) What is the minimum frequency of light necessary to emit electrons from sodium via the photoelectric effect? (b) What is the wavelength of this light? (c) If sodium is irradiated with light of \(405 \mathrm{nm},\) what is the maximum possible kinetic energy of the emitted electrons? (d) What is the maximum number of electrons that can be freed by a burst of light whose total energy is \(1.00 \mu \mathrm{J}\) ?

Microwave ovens use microwave radiation to heat food. The energy of the microwaves is absorbed by water molecules in food and then transferred to other components of the food. (a) Suppose that the microwave radiation has a wavelength of \(11.2 \mathrm{~cm} .\) How many photons are required to heat \(200 \mathrm{~mL}\) of coffee from \(23^{\circ} \mathrm{C}\) to \(60^{\circ} \mathrm{C} ?\) (b) Suppose the microwave's power is \(900 \mathrm{~W}\) ( 1 Watt \(=1\) joule-second). How long would you have to heat the coffee in part (a)?

(a) What is the frequency of radiation that has a wavelength of \(10 \mu \mathrm{m},\) about the size of a bacterium? (b) What is the wavelength of radiation that has a frequency of \(5.50 \times 10^{14} \mathrm{~s}^{-1}\) ? (c) Would the radiations in part (a) or part (b) be visible to the human eye? (d) What distance does electromagnetic radiation travel in \(50.0 \mu \mathrm{s} ?\)

The first 25 years of the twentieth century were momentous for the rapid pace of change in scientists' understanding of the nature of matter. (a) How did Rutherford's experiments on the scattering of \(\alpha\) particles by a gold foil set the stage for Bohr's theory of the hydrogen atom? (b) In what ways is de Broglie's hypothesis, as it applies to electrons, consistent with J. J. Thomson's conclusion that the electron has mass? In what sense is it consistent with proposals preceding Thomson's work that the cathode rays are a wave phenomenon?
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