CH4b - 4-11...

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Unformatted text preview: 4-11 1"=R1nf2#1ni2$%&(). For the Balmer series, nf=2; ni=3, 4, 5, K. The first three lines in the series have wavelengths given by 1"=R122#1n2$%&()where R=1.097 37"107m#1. 1st line: 1"=R14#19$%&()=536$%&()R; "=365R=656.112 nm2nd line: 1"=R14#116$%&()=316$%&()R; "=163R=486.009 nm3rd line: 1"=R14#125$%&()=21100$%&()R; "=10021R=433.937 nm4-12 1"=R1#1n2$%&()where n=2, 3, 4, Kand R=1.097 3732"107m#1; For n=2: "=R#11#122$%&()#1=1.215 02*10#7m=121.502 nm UV( )For n=3: "=R#11#132$%&()#1=1.02517*10#7m=102.517 nm UV( )For n=4: "=R#11#142$%&()#1=1.972 018*10#7m=97.201 8 nm UV( )4-14 (a) rn=n2h2meke2; where n=1, 2, 3, Krn=n21.055"10#34Js( )29.11"10#31kg( )9.0"199Nm2C2( )1.6"10#19C( )2=0.052 9 nm( )n2For n=1: rn=0.052 9 nmFor n=2: rn=0.2121 nmFor n=3: rn=0.477 2 nm(b) From Equation 4.26, v=ke2mer"#$%&1 2v1=8.99"109Nm2C2( )1.60"10#19C( )29.11"10#31kg( )0.052 9"10#9m( )$%&&&()))1 2=2.19"106m sv2=1.09"106m sv3=7.28"105m s(c) As c=3.0"108m s, v<<cand no relativistic correction is necessary. 4-15 (a) The energy levels of a hydrogen-like ion whose charge number is 2 is given by En="13.6 eV( )Z2n2="54.4 eVn2for Z=2. He+( )0 E3="6.04 eVE2="13.6 eVSo E1="54.4 eVE2="13.6 eVE3="6.04 eV, etc....
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CH4b - 4-11...

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