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School
Southwestern College, California**We aren't endorsed by this school
Course
BIOL 265
Subject
Chemistry
Date
Dec 17, 2024
Pages
3
Uploaded by BrigadierTankPelican34
R _ 2n2μZ2e4 H-(4ne0)2h2 1 1 1 -μ = -m + --' where me = mass of electron and mnucleus = mass of nucleus e mnucleus RH= 2.17868891 x 10-10 J = 1.09677759 x 107 m-1 Note that the value of RH in m-1 is the energy in wavenumbers; this what you get when you divide RH in Joules by h and c (Planck's constant and speed of light); it corresponds to 11A, the number of waves per meter. Oftentimes cm-1 is used. You may remember seeing this on IR spectra. 1. Knowing that E = RH(1ln? -1/nh2), please calculate the energy and wavelength of Two emission lines in the hydrogen spectrum. These two lines correspond the energy emitted when an electron in a hydrogen atom goes from nh = 4 to n1 = 3 and nh = 3 to n1 = 1. For each transition, specify what range of electromagnetic spectrum corresponds to the transition (UV, Vis, IR, etc). _L) ,.,t-\? -'2..?-s -:. I'-___., e, ~ti ( -~2-) E,"' ( 1.D9\077S4 "\() 1)( --t ) E.--0·<F\o7~59i-\ti::i-'X_-¼-111;, J ,,,q.74?'\\ \cm 'Ii l b 1, : '1-7~'1\1<\0" 2. What is the emission wavelength for an electron falling from the vacuum level (n = 00) to the lowest energy level in a hydrogen atom? Use the Rydberg equation and the numerical values for the Rydberg constant RH given above. In which part of the electromagnetic spectrum is this? t) • ~H (:? -;Z' ) ' :: t .OCl0'6 t-lOq (Y),l (_,') -;; ' (Ybi-,.I O 4
3· Use ~ohr's expression for the Rydberg constant to estimate the n = 00 to n = 1 transition for 150 . Z (nuclear charge) andμ (the reduced mass) are the only things in the Rydberg constant expression that need to be changed from the last calculation; everything else shou_ld be the same. Assume just one electron-not realistic, but it should give you roughly the_ nght answer. There is an easy way and a hard way to do this-do it the easy way! In which part of the electromagnetic spectrum is this? This was the sort of emission that Moseley observed to determine the atomic numbers of the elements. --2,\ 2. J , r-i ?...e .:\ ...1.. _L ...J.----~''--"-'-=-1.,,.:k::...o,::::..:~t?.---N -:;: {Y\ t=.. + '("(' "v1c. ,e.,u. "--_,L'.f-n_ Zea lV> 5. What is the energy difference between the n = 2 and n = 1 levels? What wavelength of light could promote an electron from the n = 1 level to the n = 2 level? W_bat range of..1b.e ele.ctrornagne1ic spectrum is this?
h~· f . 15 the energy difference between the n = 3 and n = 2 levels? What wavelength 0 11 ht could promote an electron from the n = 2 level to the n = 3 level? What range of the electromagnetic spectrum is this? -v\ 1c, 2--' l1. ')' l \,, . lo ii,, ,_ I D -"') "2. --:;; .,. (_g ' "' C< ·Y'\ ' I 0 • l'-' 1aci2J.:.1~\v\D?..'')(o.eaoi1-10 ) I I e :,-; l '2:>''? Lto.\o1Jo ll\t)- ~4)L , q• "? 2,, 1. <1 1 oq-,,~ 141 •1c:tl o ·ID~' 10 ) - 1-::\ -I ,a--\\£) -lo , c,c(~ q 't-\ a C i;: r \ st§D\4 ~c .., v :,-'--:'2. , · I VJ' (o'lG ' \().,, -") l -i,' 1o' 1 \r\c\.~---~\ >-;-., (Cb. -:i,'-t>lo\ Y. \() J 7. Now calculate the difference between the n = 2 and n = 1 levels of an electron in a onedimensional box which is 1.2 nm (12 A) in length. What wavelength of light could promote an electron from the n = 1 level to the n = 2 level in this system? What range of the electromagnetic spectrum is this? How does this compare to your answer to question 2? ( O .1 '7-'f l D-'I ) \ D"" -