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hw 9 with solutions

What wavelength in a microwave spectrum will this

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Also consider a J=2 to J=3 transition. What wavelength in a microwave spectrum will this transition be observed at? 5) Consider the symmetric rotor NH 3 with two defined moments of inertia; I=4.41x10 -47 kg m 2 and 2.81x10 -47 . i) Which I value is associated with the principal axis? ii) What if the value of the rotational constant A and B? iii) Calculate the lowest nonzero rotational energy of NH 3 . iv) What is the next lowest nonzero rotational energy? 6) Consider NO that has a bond distance of 115 pm. Where will the first 3 lines of the pure rotational spectra of this molecule appear?
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-- cHi 2-3 '"2- - - Pr--o'b\.c..- S:c.+ :tt:- /0 ([) ~ \) N\--\~ I =- 4. 'f ,)( ",- 't'1 ~ 'L-- ;::: 2 ~~, 'JC. (0- Y"1- ~ --~ ;.) }J't.1.~ ~~ o'o\o 'tc- Sc \ ..z- , I > .:T.L- 11c..",-,,-<- 1;, -:::: lI.'" I >t:: (O -.,~ ~J . "2. 4- 2- - -"t;f -I-~ =- 2.c?,)({() ~ ,W\L r--., - -"'\ 1\ (fj, f.z~xIO->" )")/2""-) ..It..A. J -- - ~~~~'(..I --'::~~,. J- -~ ., 1+ ;;::. <{(7L.:T,( - ':Irr (2..Cf~)(lo6'"'/s.)( 4. '-I!>C.IO-'-J9 t:J't"-~) :: t~".f,5'""~_\:: 6.3(5 c;' 6 '=:. --:B:.-- - (b . ~ ~ ~ Iv-)""' T. ~ 12 TT) I.f IT c. r..J- - e--- -:- lIT[ (1.~~~'~ ""'/S(2,.81)(.'(I"'f~) I -I --:: I () ~,()~ 1\'\ - =- / () I 00 c. IIA AA;') t(;;,wt.-~+ 't'\oV'- Q~r-o l5 T-= ( lA.~ k:::-' ) S""c..~ r--., F(T,KJ-='" 8T(T+I) + (A-.I3.J/;:::"2... ~ > 5>-/\ --~ -- ,
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~ (i) ~ f,o~,.+ -= lo.()O (1)(/+1) + (t.38-IO,OO)(I)'Z.. o/\O~ 7c.ro F =.:2 0, C> 0 ~ L""' -I - ~ , 6'2. c,... -I = It, 38 c ~ -, '~~J\ \I\()" - .f.c""' h ( ~ J'f )( 'Z. ~ , ~ I~ 8 W\ loS C L V-, ) .e = ~ ) ;:' 6, 6") ~ I c) - r; .s - . - -A ! b "3> 8 Iv' lo\olc.~;" I ~ > c' ;\\ ~ ov\ "'t~r--(..;) -"2 r- -""Z.."L - :) . 2. ~ x /0 -J ~ .A\\) )Jc..~+ lo,"",~~-\ 1~ W\..,.<- "'~O- o..~ ~=-::J- .so r =- /O,DO (1)(/+-1) +- C> - /- := '2 0 «:) 0 C.- ~ - \ or- e t\c..,..\- = (t . b~,)( 1",-3,"/ )I}) (1-,<jc,I(./r;"""'/sY '2 &I (:)0 ~-') 1o"'c-~1(-" ... z.z. --- -:- '?" 9b x /0 .J ~ jj .1 ; t t i ! ! ,
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- Q) ~ 2-) FDC"" (,'"c._r J' (.)lc ~-'C- J:::=..,A.(.;2"Z- / ~ ( _2r) (J1, f\'\ '- ~/I./ ~ I,t.' ~ Ic>- 2 .k~)\.. /6 )< /,6")( Ie) A.:: ~ ':::' - CJ - I'k f 1" M"l. ( I Y )(. I, ~ (, ~ (()- 2. 'f ) +- (I ~ It ). b' y I" - 2 -1 ) I -1 fo -:::: I 2 I.-( x to f:: d -;- = ( I - 2. 6 /:-: ""' ( -/2 ) '"Z- ~ fr '2 \.f)(. /(.) "J J / / S- X 10 IV\. ~ ~ == /, ~ '{ x 10 - k d IV'"t- t8 -::: L-- -= (l, t ~ Jllc,;' ')."f /2 n ) «lIT!:.. (1,6'"/x/D -'I6F j 1-) ~ 11 (~-;e)I~~.~~.':'~:':'4~ ~:; I -=7-J,y rh-1 -= /, "7l-14 c.~-\ '"1 t9I -'Z3 -- ::: ::> I ~ -r ~ /0 ...) U~'\4 ~ oJ j\'<-O..t~V\.t.i ~ ~ S"", 13. x/O l°.s-' C) r S ,~ x 10" 5-1 -==- S-I ~ GH-:;;;- ~ /~ ":3>-li.l\.c.":> o ~p-e.c r- c ~ ~~IY5, c..,,\~ 6B . : +~t..'-\ t f'p.e.o..r- 0 \- /0 "Z. 6 ). '2- D '5""2) ~ V"l J 3 0 1-- f:> (, I-l.:t- ;-- - ~.
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