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Ch8. Molecules Introduction (inert gas)

(molecules)(liquid)(solid)

energy

The Molecular Bond:

1.(covalent bond) H2

H2 + 4.5eV -> H + H

2

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2.(ionic bond) Salt (NaCl)NaCl crystal

molecule HCl

3. exclusion principle

( minor

)

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Electron sharing H+2 proton potential barrier(or box)

wave funtiontunneling

share

H+2

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System Energy H+2 proton R

H+2(Estotal )= (Up) + (Es)

2

04p

eUR

=

, 0pU R= 0,pU R= and

( 13.6 4) 54.4 , 0sE eV eV R= = = He+ ion = (2)2EH ( 13.6 ) ( 2.65 ) 16.3 ,sE eV eV eV R= + =

( H2+ + 2.65eV(bond energy) -> H + H+

-16.3eV + 2.65eV -> -13.6eV + 0 )

R = 1.06 x 10-10m

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The Hydrogen Molecule Exclusion principle the spins of the electrons must be

antiparallel

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Complex Molecule Their geometry depends on the wave functions of the outer electrons of

their atoms. x-ray spectrachemical bonding

( valence electron)inner shell electrons

s p

wave funtion bonding

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12

, ,ss pp pp ()

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H2O H O sp ()

CH4(methane) C HC 2s 2p3sp ()

C2H4(ethylene) C6H6(benzene)2sp hybrid oorbitals

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Rotational Energy Level energy state(

)

1.Rotational state

Typical energy interval ~ 10-3eV. These

states are in the microwave region with wavelengths of 0.1mm to 1cm.The

absorption by water molecules of rotational energy from microwaves

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underlies the operation of microwave ovens.

2.Vibrational state;

energy stateTypical energy interval ~ 0.1eV. Vibrational

spectra are in the infrared region with wavelengths of 1um to 0.1mm.

3.Molecular electronic statesenergy level eVthe

corresponding spectra are in the visible and ultraviolet regions.

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()(moment of inertia) 2 2

1 1 2 2I m r m r= + 1 1 2 2m r m r=

2 ' 21 21 2

1 2

( )m mI r r m Rm m

= + =+

where ' 1 2

1 2

m mmm m

=+ = reduced mass, 1 2R r r= +

angular momentum

( 1)L I J J= = + -> ( 1) /J J I = +

the energy of rotating molecule is

221 ( 1)

2 2JJ JE I

I += =

Example: The carbon monoxide (CO) molecule has a bond length R of 0.113nm and

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the masses of the 12C and 16O atoms are respectively 1.99x10-26kg. Find (a)

the energy and (b) the angular velocity of the CO molecule when it is

in its lowest rotational state.

Solution:

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Rotational Spectra Rotational energy states transition spectra

electric dipole mement absorb or emit

H2 or CO2, CH4()

Rotational transition selection rule()

1J =

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rotational spectrum(equally spaced lines)

Example: In CO the J=0 -> J=1 absorption line occurs at a frequency of 1.15x1011Hz.

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What is the bond length of the CO molecule?

Solution:

Vibrational Energy Levels A molecule can have many different modes of vibration

(Harmonic oscillation)

()

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22

20 0

1 ( )2

U U k R R + (Restoring force)(Hookes law)

0( )dUF k R RdR

=

0 '

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kfm

=

0 '

1 1

2 2)( ) ( kE n hf n

m= + = +

0,1, 2,3,n = vibrational quantum number

the lowest vibration state n = 0 has the zero-point energy

0 012

E hf= uncertainty principle

Vibrational Spectra Selection rule

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1n = vibrational state rotational stateenergy spacing?

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Example: When CO is dissolved in liquid carbon tetrachloride, infrared radiation

of frequency 6.42x1013 Hz is absorbed. Carbon tetrachloride by itself

is transparent at this frequency, so the absorption must be due to the

CO. (a) What is the force constant of the bond in the CO molecule? (b)

What is the spacing between its vibrational energy level?

Solution:

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kT ~ 0.026eV 0.266eV vibrational energy

H2O()

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CO2 vibrational mode

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CO2(Vibration mode)

greenhouse effect

-OH-NH2-SH vibration frequency

thioacetic acid

CH3CO-SH CH3CS-OH

Electronic Spectra of Molecules

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() electron energy level

transition

Fluorescence

ground state excited

state excited

state vibrational transition excited state transit

ground state (

)

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31

()

LED()

Phosphorescence

singlet ground state(S=0) singlet excited state shift

energy level triplet excited state(S=1) selection rule

triplet excited state singlet ground state

transition