mp-Chapt-9-sol - Chapter 9 Problem Solutions 1 At what...

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Inha University Department of Physics Chapter 9 Problem Solutions 1. At what temperature would one in a thousand of the atoms in a gas of atomic hydrogen be in the n =2 energy level? 2 8 1 2 = = ) ( , ) ( e e g g kT kT e e n n / / ) ( ) ( ) ( 1 1 2 3 1 2 4 4 1000 1 e e e e e = = = - - K 10 43 1 4000 eV/K 10 62 8 eV 6 13 4 3 4000 4 3 1 4 5 1 × = × = - = - . ) )(ln . ( ) . )( / ( ln ) )( / ( e k T eV 6 13 and 4 1 1 2 . , / - = = e e e Then, where 3. The 3 2 P l/2 first excited sate in sodium is 2.093 eV above the 3 2 S 1/2 ground state. Find the ratio between the numbers of atoms in each state in sodium vapor at l200 K. (see Example 7.6.) 9 5 10 86 4 K 1200 eV/K 10 62 8 eV 09 2 1 3 - - × = × - . ) )( . ( . exp sol sol multiplicity of P -level : 2 L +1=3, multiplicity of S -level : 1 The ratio of the numbers of atoms in the states is then,
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Inha University Department of Physics 5. The moment of inertia of the H 2 molecule is 4.64 10 -48 kg·m 2 . (a) Find the relative popula- tions of the J =0,1,2,3, and 4 rotational states at 300 K. (b) can the populations of the J =2 and J =3 states ever be equal? If so, at what temperature does this occur? I J J J J g J 2 1 1 2 2 h ) ( , ) ( + = + = e 0 0 = = J e ) ( ) ( ) ( ] . )[ ( ) )( . )( . ( ) . ( exp ) ( exp ) ( ) ( exp ) ( ) ( ) ( 1 1 23 2 48 2 34 1 2 2 749 0 1 2 K 300 J/K 10 38 1 m kg 10 64 4 2 s J 10 06 1 1 2 2 1 2 2 1 1 2 0 + + - - - + + = × × × - + = - + = + - + = = J J J J J J J J IkT J IkT J J J J N J N h h Applying this expression to J=0, 1, 2, 3, and 4 gives, respectively, 1 exactly, 1.68, 0.880, 0.217, and 0.0275. (b) Introduce the dimensionless parameter . Then, for the populations of the J =2 and J =3 states to be equal, 7 5 6 and 7 5 7 5 6 12 6 ln ln , = = = x x x x Using , and solving for T , ) / ( - ) / ( IkT x 5 7 7 5 and 2 2 ln ln / ln = - = h sol (a)
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Department of Physics K 10 55 1 4 1 J/K 10 38 1 m kg 10 64 4 2 s J 10 05 1 6 5 7 2 6 3 23 2 48 2 34 2 × = × × × = = - - - . ) . ln( ) . )( . ( ) . ( ) / ln( Ik T h 7. Find and v rms for an assembly of two molecules, one with a speed of 1.00 m/s and the other with a speed of 3.00 m/s. v (m/s) 24 2 00 3 00 1 (m/s) 00 2 00 3 00 1 2 2 2 1 2 1 . ] . . [ . ) . . ( = + = = + = rms v v 9. At what temperature will the average molecular kinetic energy in gaseous hydrogen equal the binding energy of a hydrogen atom? kT KE 2 3 = solving for T with 1 E KE - = K 10 05 1 eV/K 10 62 8 eV 6 13 3 2 3 2 5 5 1 × = × = - = - . ) . ( ) . )( / ( k
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This note was uploaded on 11/29/2010 for the course PHY 111 taught by Professor Kim during the Spring '10 term at 카이스트, 한국과학기술원.

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mp-Chapt-9-sol - Chapter 9 Problem Solutions 1 At what...

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