Question #89cc5
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"An electron in a hydrogen atom drops from energy level n=5 to n=3. What is the energy transition using the Rydberg equation?"
We know that the moment of inertia #I# of a disk is related with its mass #M# and radius #R# as follows
#color(blue)(I=1/2MR^2.......................[1])#
Now #M=4/3piR^3drho#
where #m->"mass" , d->"thickness" and rho ->"density"#
#=>R=((3M)/(4pidrho))^(1/3)#
#=>R^2=((3M)/(4pidrho))^(2/3)#
Hence equation [1] becomes
#color(green)(I=1/2Mxx((3M)/(4pidrho))^(2/3).......................[2])#
Now if #M and d # are remaining constant as per given condition then
#color(red)(Iprop1/rho^(2/3).......................[3])#
If the moment of inertia of first disk of density #rho_1=7.2"g/"cm^3# be #I_1# and the moment of inertia of 2nd disk of density #rho_2=8.9"g/"cm^3# be #I_2# then the ratio of moment of inertia of two disks is given by
#color(blue)(I_1/I_2=(rho_2/rho_1)^(2/3)=(8.9/7.2)^(2/3)~~1.15)#
