Introduction to Molecular Thermodynamics

Robert M. Hanson, Susan Green

Chapter 3 Energy Levels in Real Chemical Systems - all with Video Answers

Educators

Chapter Questions

Problem 1

Calculate the de Broglie wavelength in meters for the following objects: (a) an electron traveling at $10^6 \mathrm{~m} / \mathrm{s}$; (b) a , baseball weighing $51 / 4$ ounces and traveling at 90 miles per hour; (c) Superman, assuming he weighs $180 \mathrm{lbs}$., traveling at a speed where he circles the earth, circumference $40,000 \mathrm{~km}$, 100 times per minute.

Crystal Wang

Numerade Educator

01:15

Problem 2

Calculate the de Broglie wavelength in meters for the following objects: (a) a proton traveling at $1.1 \times 10^4 \mathrm{~m} / \mathrm{s}$; (b) a basketball weighing $600 \mathrm{~g}$ and traveling $1.8 \mathrm{~m} / \mathrm{s}$; (c) an aircraft weighing 800,000 lbs and traveling at 583 miles $/ \mathrm{hr}$.

Crystal Wang

Numerade Educator

02:37

Problem 3

lculate the energy of the first three levels of (a) an electron confined to a one-dimensional box of length $100 \mathrm{pm}$; (b) a proton confined to the same box.

Suzanne W.

Numerade Educator

05:44

Problem 4

Calculate the energy of the first three levels of (a) an electron confined to a one-dimensional box of length 500 pm; (b) a proton confined to the same box.

Robert Zaballa

Numerade Educator

05:44

Problem 5

Calculate the energy of the first three levels of (a) an electron confined to a one-dimensional box of length $2000 \mathrm{Pm}$; (b) a proton confined to the same box.

Robert Zaballa

Numerade Educator

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Problem 6

Using Equation 3.9 and the Boltzmann equation, calculate (a) the energies of the first, two electrodnic levels of the hydrogen atom; (b) the number of atoms in the first excited electronic energy level $(n=2)$ for a mole of hydrogen atoms at equilibrium at $5700^{\circ} \mathrm{C}$ (the temperature of the surface of the sun); (c) the same for a mole of hydrogen atoms at $-223^{\circ} \mathrm{C}$ (the temperature on the surface of Pluto); (d) the temperature required for roughly $10 \%$ of the hydrogen atoms to be in the first excited electronic state (i.c., $n_2 / n_1=1 / 9$ ).

Lainey Roebuck

Numerade Educator

05:33

Problem 7

For a belium atom the difference in energy between the first two electronic energy levels, $\Delta \varepsilon_{0,1}$, is known to be 19.82 $\mathrm{eV}$. ( $1 \mathrm{eV}$, or electron volt, is $1.602 \times 10^{-19}$ joules.) (a) For a mole of helium atoms at $5700^{\circ} \mathrm{C}$, the temperature of the surface of the sun, how many atoms are in thle first excited electronic energy level? (b) How does this number change if the mole of helium atoms is now at $-223^{\circ} \mathrm{C}$, the temperature on the surface of Pluto? (c) What does the temperature need to be for $10 \%$ of helium atoms to be in the first excited electronic state (i.e. $\left.n_2 / n_1=1 / 9\right) ?$

Christopher Provencher

Numerade Educator

03:17

Problem 8

With respect to the hydrogen atom and Figure 3.4 and using Equations 3.1. 3.2, and 3.9, calculate the wavelength in nanometers associated with (a) the lowest-energy Balmer line; (b) the lowest-energy infrared emission; (c) the ionization energy.

Ren Jie Tuieng

Numerade Educator

02:10

Problem 9

Draw Lewis structures and calculate $\mu$ for $\mathrm{F}_2$ and $\mathrm{N}_2$, and use this information to explain why the vibrational energy levels in ${ }^{19} \mathrm{~F}_2$ are more closely spaced than those in ${ }^{14} \mathrm{~N}_2$.

Khoobchandra Agrawal

Numerade Educator

02:15

Problem 10

Draw Lewis structures and calculate $\mu$ for $\mathrm{H}_2$ and $\mathrm{N}_2$. and use this information to explain why the vibrational energy levels in ${ }^1 \mathrm{H}_2$ are further apart in energy than those in ${ }^{14} \mathrm{~N}_2$.

Ashley Brady

Numerade Educator

01:04

Problem 11

Draw Lewis structures and calculate $\mu$ for ${ }^1 \mathrm{H}_2$ and ${ }^2 \mathrm{H}_2$, and use this information to explain why the vibrational energy levels in ${ }^2 \mathrm{H}_2$ are more closely spaced than those in ${ }^3 \mathrm{H}_2$.

Crystal Wang

Numerade Educator

01:28

Problem 12

Which of the following would be the expected effect on the difference in energy of the lowest two vibrational levels ( $\Delta \varepsilon_{\text {vib }}$ ) in a molecule $\mathrm{HX}$ if hydrogen is replaced by deuterium, ${ }^2 \mathrm{H}$ ? Explain.
(a) $\Delta \varepsilon_{\text {vit }}$ will double.
(b) $\Delta \varepsilon_{\text {val }}$ will halve.
(c) $\Delta \varepsilon_{\text {vib }}$ will go up by roughly a factor of $\sqrt{2}$.
(d) $\Delta \varepsilon_{\text {vib }}$ will go down by roughly a factor of $\sqrt{2}$.

Mayukh Banik

Numerade Educator

Problem 13

Argue for or against each statement based on the following data:
$$
\begin{array}{llll}
{ }^1 \mathrm{H}{ }^{127} \mathrm{I} & k_{\mathrm{f}}=291 \mathrm{~kg} / \mathrm{s}^2 & \mu=0.992 \mathrm{amu} & R=161 \mathrm{pm} \\
{ }^1 \mathrm{H}^{79} \mathrm{Br} & k_{\mathrm{h}}=408 \mathrm{~kg} / \mathrm{s}^2 & \mu=0.994 \mathrm{amu} & R=141 \mathrm{pm} \\
{ }^{14} \mathrm{~N}_2 & k_{\mathrm{f}}=2340 \mathrm{~kg} / \mathrm{s}^2, & \mu=7: 0 \mathrm{amu} & R=110 \mathrm{pm} \\
{ }^{12} \mathrm{C}^{16} \mathrm{O} & k_{\mathrm{f}}=1860 \mathrm{~kg} / \mathrm{s}^2, & \mu=6.9 \mathrm{amu} & R=113 \mathrm{pm} \\
{ }^{14} \mathrm{~N}^{16} \mathrm{O} & k_{\mathrm{r}}=1550 \mathrm{~kg} / \mathrm{s}^2 & \mu=7.5 \mathrm{amu} & R=115 \mathrm{pm} \\
{ }^{16} \mathrm{O}_2 & k_{\mathrm{f}}=1140 \mathrm{~kg} / \mathrm{s}^2 & \mu=8.0 \mathrm{amu} & R=121 \mathrm{pm} \\
{ }^{19} \mathrm{~F}_2 & k_{\mathrm{f}}=450 \mathrm{~kg} / \mathrm{s}^2 & \mu=9.5 \mathrm{amu} & R=141 \mathrm{pm}
\end{array}
$$
(a) ${ }^{16} \mathrm{O}_2$ has more closely spaced vibrational energy levels than ${ }^{14} \mathrm{~N}^{16} \mathrm{O}$.
(b) ${ }^{14} \mathrm{~N}_2$ has more closely spaced vibrational energy levels than ${ }^{16} \mathrm{O}_2$.
(c) ${ }^1 \mathrm{t}^9 \mathrm{Br}$ has more closely spaced vibrational energy levels than ${ }^{14} \mathrm{~N}_2$.
(d) ${ }^1 \mathrm{H}^{127} \mathrm{I}$ has more closely spaced vibrational energy levels than ${ }^{14} \mathrm{~N}_2$.

Check back soon!

01:50

Problem 14

Calculate and compare the vibrational frequency $v$ for the following isotopes of $\mathrm{HCl}$ (assume $k_1=478 \mathrm{~kg} / \mathrm{s}^2$ ): (a) ${ }^1 \mathrm{H}^{35} \mathrm{Cl}$ (b) ${ }^1 \mathrm{H}^{37} \mathrm{Cl}$ (c) ${ }^2 \mathrm{H}^{35} \mathrm{Cl}$ (d) ${ }^2 \mathrm{H}^{37} \mathrm{Cl}$.

Lottie Adams

Numerade Educator

02:09

Problem 15

Calculate the vibrational frequency $\nu$ for each of the following isotopes of $\mathrm{HBr}\left(k_{\mathrm{f}}=290 \mathrm{~kg} / \mathrm{s}^2\right):(\mathrm{a})^1 \mathrm{H}^{79} \mathrm{Br}$ (b) ${ }^1 \mathrm{H}^{81} \mathrm{Br}$ (c) ${ }^2 \mathrm{H}^{79} \mathrm{Br}$ (d) ${ }^2 \mathrm{H}^{81} \mathrm{Br}$.

Lottie Adams

Numerade Educator

05:34

Problem 16

Assuming $k_f=478 \mathrm{~kg} / \mathrm{s}^2$, calculate and compare the fraction of molecules in the first excited vibrational state at $1000 \mathrm{~K}$ for (a) ${ }^1 \mathrm{H}^{35} \mathrm{Cl}$ (b) ${ }^1 \mathrm{H}^{37} \mathrm{Cl}$ (c) ${ }^2 \mathrm{H}^{35} \mathrm{Cl}$ (d) ${ }^2 \mathrm{H}^{37} \mathrm{Cl}$.

Eduard Sanchez

Numerade Educator

02:09

Problem 17

At $1000 \mathrm{~K}$, calculate the percentage of molecules in the first excited vibrational state for each of the following isotopes $\left(k_{\mathrm{f}}=290 \mathrm{~kg} / \mathrm{s}^2\right):(\mathrm{a}){ }^1 \mathrm{H}^{81} \mathrm{Br}(\mathrm{b})^2 \mathrm{H}^{79} \mathrm{Br}(\mathrm{c})^2 \mathrm{H}^{81} \mathrm{Br}$

Lottie Adams

Numerade Educator

02:09

Problem 18

Roughly, what does the temperature need to be for $10 \%$ of ${ }^1 \mathrm{H}^{79} \mathrm{Br}$ molecules to be in the first excited vibrational energy level $\left(k_f=290 \mathrm{~kg} / \mathrm{s}^2\right)$ ?

Lottie Adams

Numerade Educator

03:29

Problem 19

Roughly what does the temperature need to be for $10 \%$ of a sample of ${ }^1 \mathrm{H}^{37} \mathrm{Cl}$ molecules to be in the first excited vibrational energy level (i.e. $n_1 / n_0=1 / 9$ )?

Prachita Kush

Numerade Educator

Problem 20

Argue for or against each statement based on the data given in Problem 3.13.
(a) ${ }^{19} \mathrm{~F}_2$ has more closely spaced rotational energy levels than ${ }^{16} \mathrm{O}_2$.
(b) ${ }^{14} \mathrm{~N}^{16} \mathrm{O}$ has more closely spaced rotational energy levels than ${ }^{12} \mathrm{C}^{16} \mathrm{O}$.
(c) ${ }^1 \mathrm{H}^{79} \mathrm{Br}$ has more closely spaced rotational energy levels than ${ }^{19} \mathrm{~F}_2$.
(d) ${ }^1 \mathrm{H}^{127} \mathrm{I}$ has more closely spaced rotational energy levels than ${ }^1 \mathrm{H}^{79} \mathrm{Br}$.

Check back soon!

01:55

Problem 21

Which of the following would be the expected effect on the difference in energy of the lowest two rotational levels $\left(\Delta \varepsilon_{\text {rot }}\right.$ ) in a molecule HX if hydrogen is replaced by deuterium, ${ }^2 \mathrm{H}$ ? Explain.
(a) $\Delta \varepsilon_{\text {rot }}$ will double.
(b) $\Delta \varepsilon_{\text {rot }}$ will go up by roughly a factor of $\sqrt{2}$.
(c) $\Delta \varepsilon_{\text {rot }}$ will halve.
(d) $\Delta \varepsilon_{\text {rox }}$ will go down by roughly a factor of $\sqrt{2}$.

Khoobchandra Agrawal

Numerade Educator

03:14

Problem 22

Rotational spectroscopy can determine the energy differences between rotational energy levels. Frequently this is used to determine the bond length of the molecule, or in the case of larger molecules the bond lengths and angles. An absorption having an energy of $7.61 \times 10^{-23} \mathrm{~J}$ was assigned to $\Delta \varepsilon_{0,1}$ of carbon monoxide, $\mathrm{CO}$. (a) Based on this information. what is the bond length of $\mathrm{CO}$ ? (b) What energy would you expect to observe for the absorption corresponding to $\Delta \varepsilon_{0,1}$ $\mathrm{CO}^{+}$, which is proposed to have a bond length $1.3 \%$ shorter than that of carbon monoxide?

Lottie Adams

Numerade Educator

04:21

Problem 23

Draw an energy level picture comparing the first three rotational energy levels in a system at $25^{\circ} \mathrm{C}$ containing 1 mole of $\mathrm{N}_2(R=110 \mathrm{pm}) \mathrm{vs}$. one containing 1 mole of $\mathrm{T}_2(R=194 \mathrm{pm})$.

Narayan Hari

Numerade Educator

07:10

Problem 24

The bond length of $\mathrm{Na}_2$ is $307.9 \mathrm{pm}$. (a) Determine the difference iff energy between the first two rotational energy levels of $\mathrm{Na}_2$. (b) $\mathrm{A}$ spectrometer used to study the rotational spectroscopy of $\mathrm{Na}_2$ can distinguish between energies that differ by $5 \times 10^{-25} \mathrm{~J}$ or more. Will this spectrometer be able to distinguish between a signal due to the transition between the first and second rotational energy levels of $\mathrm{Na}_2$ and those of $\mathrm{Na}_2^{+}$, which has a bond length that is $45.1 \mathrm{pm}$ longer than the bond length of $\mathrm{Na}_2$ ?

Dading Chen

Numerade Educator

06:17

Problem 25

The bond length of $\mathrm{SiO}$ is $151 \mathrm{pm}$. (a) Determine the difference in energy between the first two rotational energy levels of SiO. (b) A spectrometer used to study the rotational spectroscopy of SiO can distinguish between energies that differ by $1 \times 10^{-25} \mathrm{~J}$ or more. Will this spectrometer be able to distinguish between a signal due to the transition between the first and second rotational energy levels of $\mathrm{SiO}$ and those of $\mathrm{SiO}^{+}$, which has a bond length that is $1 \mathrm{pm}$ shorter than the bond length of SiO?

Prachita Kush

Numerade Educator

00:54

Problem 26

Determine the difference in energy between the first two translational energy levels, $\Delta \varepsilon_{1,1,1,2,1,1}$, of a system of $\mathrm{He}$ atoms confined to a cubical 15-L tank.

Zachary Warner

Numerade Educator

02:48

Problem 27

Determine the difference in energy between the first two translational energy levels, $\Delta \varepsilon_{1,1,1,2,1,1}$, of a system of Ar atoms confined to a cubical $15-\mathrm{L}$ tank.

Hafiz Shahzaib

Numerade Educator

00:57

Problem 28

Argue for or against:
(a) Xe has more closely spaced translational energy levels than $\mathrm{Kr}$.
(b) He has more widely spaced translational energy levels than $\mathrm{H}$.
(c) $\mathrm{SF}_6$ has more closely spaced translational energy levels than $\mathrm{CH}_4$.

Hast Aggarwal

Numerade Educator

01:53

Problem 29

Which of the following (if any) would be the expected effect on the difference in energy of the lowest two translational levels ( $\left.\Delta \varepsilon_{\text {trass }}\right)$ in a molecule $H X$ if hydrogen is replaced by deuterium, ${ }^2 \mathrm{H}$ ? Explain.
(a) $\Delta \varepsilon_{\text {trans }}$ will double.
(b) $\Delta \varepsilon_{\text {mans }}$ will halve.
(c) $\Delta \varepsilon_{\text {trans }}$ will go up by roughly a factor of 4 .
(d) $\Delta \varepsilon_{\text {trans }}$ will go down by roughly a factor of 4 .

Kartik Indoliya

Numerade Educator

07:18

Problem 30

A A dust mote weighing $1 \mu \mathrm{g}$ and a hydrogen atom are trapped in a $1 \mathrm{~cm}^3$ cubical vial. What is the separation between the translational energy levels of (a) the dus.mote? (b) the hydrogen atom?

Ommair Ishaque

Numerade Educator

01:04

Problem 31

Complete the following table summarizing the properties of electronic, vibrational, rotational, and translational energy.
$$
\begin{array}{lllll}
\begin{array}{l}
\text { Type of } \\
\text { Energy }
\end{array} & \begin{array}{l}
\text { Approx- } \\
\text { imate Size } \\
\text { of } \Delta \varepsilon
\end{array} & \begin{array}{l}
\text { First } \\
\text { Quantum } \\
\text { Number }
\end{array} & \begin{array}{l}
\text { Mass/Box } \\
\text { Constraint } \\
\text { Term }
\end{array} & \begin{array}{l}
\text { Present in }
\end{array} \\
\hline \text { Electronic } & 10^{-18} \mathrm{~J} & 1 & 1 / m_e a_o^2 & \begin{array}{l}
\text { solids, liquids, } \\
\text { gas, all atoms, } \\
\text { all molecules }
\end{array} \\
\hline \text { Vibrational } & & & & \\
\hline \text { Rotational } & & & & \\
\hline \text { Translational } & & & & \\
\hline
\end{array}
$$

Adriano Chikande

Numerade Educator

01:49

Problem 32

The following table is all messed up. Match the spectrum region on the left with the appropriate characteristic in each column. (The spectral regions are listed here in increasing order of energy.)
$$
\begin{array}{|c|c|c|c|}
\hline \begin{array}{l}
\text { Spectral } \\
\text { Region }
\end{array} & \begin{array}{l}
\text { Approximate } \\
\text { Frequency } \\
\text { Range }
\end{array} & \begin{array}{l}
\text { Approximate } \\
\text { Wavelength } \\
\text { Range }
\end{array} & \begin{array}{l}
\text { Typical } \\
\text { Absorption }
\end{array} \\
\hline \text { (a) Microwave } & \begin{array}{l}
\begin{array}{l}
10^9 \text { to } \\
10^{11} \mathrm{~s}^{-1}
\end{array}
\end{array} & \begin{array}{l}
\begin{array}{l}
7 \times 10^{-7} \text { to } \\
4 \times 10^{-7} \mathrm{~m}
\end{array}
\end{array} & \text { rotational } \\
\hline \text { (b) Far Infrared } & \begin{array}{l}
\begin{array}{l}
10^{15} \text { to } \\
10^{16} \mathrm{~s}^{-1}
\end{array}
\end{array} & \begin{array}{l}
\begin{array}{l}
10^{-5} \text { to } \\
7 \times 10^{-7} \mathrm{~m}
\end{array}
\end{array} & \text { elcctronic } \\
\hline \text { (c) Infrared } & \begin{array}{l}
\begin{array}{l}
10^{14} \text { to } \\
10^{15} \mathrm{~s}^{-1}
\end{array}
\end{array} & \begin{array}{l}
\begin{array}{l}
0.1 \text { to } \\
0.001 \mathrm{~m}
\end{array}
\end{array} & \text { vibrational } \\
\hline \text { (d) Visible } & \begin{array}{l}
\begin{array}{l}
10^{13} \text { to } \\
10^{14} \mathrm{~s}^{-1}
\end{array}
\end{array} & \begin{array}{l}
\begin{array}{l}
4 \times 10^{-7} \text { to } \\
10^{-8} \mathrm{~m}
\end{array}
\end{array} & \text { electronic } \\
\hline \text { (e) Ult } & \begin{array}{l}
\begin{array}{l}
10^{11} \text { to } \\
10^{13} \mathrm{~s}^{-1}
\end{array}
\end{array} & \begin{array}{l}
\begin{array}{l}
0.001 \text { to } \\
10^{-5} \mathrm{~m}
\end{array}
\end{array} & \text { rotational } \\
\hline
\end{array}
$$

Amita Prajapat

Numerade Educator

00:31

Problem 33

Which types of energy (electronic, vibrational, rotational, and/or translational) (a) are unique to molecules? (b) are not found in solids? (c) have the largest energy separations between levels? (d) have the smallest separations between levels?

Dading Chen

Numerade Educator

01:35

Problem 34

Indicate in the blank whether the statement is true or false. Explain your reasoning.
(a) $\qquad$ Rotational energy levels are generally more closely spaced than vibrational levels.
(b) $\qquad$ The reduced mass of a two-body system is always less than the smaller mass.
(c) $\qquad$ The translational energy levels in $\mathrm{H}_2$ are more closely spaced than those in $\mathrm{H}_2 \mathrm{O}$.
(d) $\qquad$ For most substances, only the lowest (ground) vibrational state is populated at $298 \mathrm{~K}$.

Nicole Smina

Numerade Educator

01:11

Problem 35

A Complete the following sentence, sclecting the correct word in each case: Expansion of a gas leads to morefless closely spaced translational/vibrational levels because . . .

Ajay Singhal

Numerade Educator

01:21

Problem 36

Complete the following sentence: At a high enough temperature every liquid will turn to gas because . . .

Lijeesh Krishnan

Numerade Educator

00:31

Problem 37

Fill in the blanks with the appropriata word: electronic, rotational, translational, or vibrational. In some cases, mơic than one answer may be correct. Indicate all correct answers: (a) $\qquad$ energy levels are ahout 10 times more closely spaced than electronic energyllevels. Consideration of reduced mass is important for calculations of (b) $\qquad$ energy. (c) $\qquad$ energy levels do not exist for molecules in the solid phase. The mass term in the (d) $\qquad$ energy equation is much smaller than the mass term for any other type of energy. (c) $\qquad$ excitation is the predominant means by which bonds are broken in ordinary chemical reactions that result from heating a substance.

Dading Chen

Numerade Educator

02:06

Problem 38

Fill in each blank with one of the following words: electronic, vibrational, rotational, or translational. In some cases, more than one answer may be correct. Indicate all correct answers: (a) $\qquad$ excitation generally requires the least energy. Reduced mass must be used for calculating (b) $\qquad$ energies because in that case the atoms of a molecule are moving closer and further away from one another. Several hundred (c) $\qquad$ energy levels for gaseous $\mathrm{HCl}$ are populated at room temperature. Microwave spectroscopy generally involves (d) $\qquad$ excitation.

Lottie Adams

Numerade Educator

02:06

Problem 39

Fill in each blank with one of the following words: electronic, vibrational, rotational, or translational. In some cases, more than one answer may be correct. Indicate all correct answers: (a) $\qquad$ excitation generally requires the most energy. Ultraviolet spectroscopy generally involves (b) $\qquad$ excitation. (c) $\qquad$ excitation is generally only possible for molecular liquids and molecular gases. Only a handful of (d) $\qquad$ energy levels for gascous $\mathrm{HCl}$ are populated at room temperature.

Lottie Adams

Numerade Educator

01:57

Problem 40

Explain (a) fluorescence (b) phosphorescence. Why might some molecules phosphoresce while others wouldn't?

Ameer Said

Numerade Educator

06:00

Problem 41

For the diatomic molecule $\mathrm{A}_2$, (a) sketch a partial energy level diagram showing two electronic states with their respective vibrational states. Clearly label the following: ground electronic state, excited electronic state, ground vibrational state (in both electronic states). (b) The transition between the ground vibrational state of the ground electronic state and the ground vibrational state of the first excited electronic state was observed at $488 \mathrm{~nm}$. Determine the separation between the electronic energy levels (in J). (c) The excited electronic state shown is kndwn to have a vibrational frequency of $2.42 \times 10^{13} \mathrm{~s}^{-1}$. Determine at what wavelength_(in nm) the transition between the ground vibrational state of the ground electronic state and the first excited vibrational state of the first excited electronic state will be observed. '

Joanna Josey

Numerade Educator

01:24

Problem 42

Most current CD and DVD players, along with many other devices, use a HeNe laser that produces light at $650 \mathrm{~nm}$. A proposed new standard for CDs would allow more data to be stored on a disk. This new,standard uses a blue light laser that produces light at $405 \mathrm{~nm}$. What is likely the major difference betweenthe chemical systems in a HeNye laser and that of a blue light lasef-that results, in the different wavelength of light being produced?

Hast Aggarwal

Numerade Educator

01:45

Problem 43

On the diagram shown below, indicate with a vertical arrow an absorption that might involve this molecule in its overall ground state bécoming
(a) vibratiorally but not rotationally excited;
(b) electronically but not vibrationally excited; .
(c) both electronically and vibrationally excited, but not rotationally excited.

Sam Limsuwannarot

Numerade Educator

04:07

Problem 44

Shown below are a molecule and its infrared spectrum. The spectrum shows an absorbance of energy when the curve drops to a lower value of "\% Transmittance." Note that infrared energy is absorbed more strongly at certain wavelengths than at others. Several bonds in the molecule (a-d) and areas of the spectrum (A-H) are labeled. The strong absorption $\mathbf{C}$ at about $5.8 \mu \mathrm{m}$ is due to stretching of bond $\mathbf{b}$. Use what you know about the effect of bond strength and atomic mass to indicate $\qquad$ The lowest-energy absorption of $\mathbf{A}, \mathbf{C}$, and $\mathbf{E}$.
$\qquad$ Of $\mathrm{B}$ and $\mathrm{E}$, the absorption more likely to be associated with bond a. $\qquad$ Of B and $\mathrm{E}$, the absorption more likely to be associated with bond $\mathrm{e}$. $\qquad$ Of $\mathrm{A}$ and $\mathrm{D}$, the absorption more likely associated with bond $\mathrm{d}$.

Katherine Mccandless

Numerade Educator

06:09

Problem 45

Explain why absorbances A and B might be so much different in energy from the others. Provided vibration of bonds $\mathbf{a}, \mathbf{b}, \mathbf{c}$, and $\mathbf{d}$ are seen as $\mathbf{A}, \mathbf{B}, \mathbf{C}$, and $\mathbf{E}$ (but not in that order), what bonds must $\mathbf{A}$ and $\mathrm{B}$ be associated with?

Eduard Sanchez

Numerade Educator

00:40

Problem 46

What are some of the special properties that metals and semiconductors have that other substances don't have? How do you explain this using the ideas of electronic energy?

Dading Chen

Numerade Educator

03:31

Problem 47

Pretend you are the electron in a hydrogen atom. Describe what you are doing (a) in the $1 s$ state (b) in the $2 p$ state (c) in the $1 \mathrm{~s}$ state absorbing $2.04 \times 10^{-18} \mathrm{~J}$ of energy.

Guilherme Barros

Numerade Educator

09:55

Problem 48

Develop an analogy relating molecules and energy levels to people having fun at a nightelub.

Naresh Bagrecha

Numerade Educator