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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~ (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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