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Usingthe Rydbergformula, calculatethe wavelengthof thefirstfourspectrallinesin theLymanseries of thehydrogenspectrum . |
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Answer» Solution :Therhdbergformulais ` ( hc )/( lamda _(if ))= (M e^4 ) /( 8 epsi_(0)^(2) h^2) ((1)/(n_(f)^(2))-(1)/( n_(i)^(2)))` Thewavelengthof thefirstfourlinesin theLyman seriescorrespond totransitions from `n_i =2` `3,4,5,` to ` n_f=1`we knowthat ` (me^4 )/( 8 epsi_(0)^(2) h^2)= 13.6 eV =21 .76 xx 10^(-19) J` therefore ` lamda_(11) = ( hc )/( 21.76xx 10^(-19) ((1)/(1) - (1)/(n_(i)^(2)))` =`( 6.625 xx 10^(-34) xx 3 xx 10^8xx n_(i)^(2) )/( 21.76xx 10^(-19) xx (n_i ^2-1))=(0.9134 n_(i)^(2) )/( (n_i ^(2)-1) ) xx 10^(-7) = ( 913 .4 n_(i)^(2 ) Å )/((n_(i)^(2) -1))` substiting`n_i = 2,3,4,5` we get `lamda_(21) = 1218 Å, lamda_(41) = 1028,lamda_(41) = 974.3Å ` and ` lamda_(51)951 .4 Å ` |
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