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let this state is n then
de broglie wavelength = h/mv
length of path = 2pir ( r is radius)
length of path = 5 (de broglie wavelength)
2pir = 5h/mv
mvr = 5h/2pi ..................1
we have , mvr = nh/2pi .............2 (bohrs quantixation of angular momentam)
comparing both
n = 5
now , maximum energy = 13.6(1-1/25)= 13.056
second maximum energy = 13.6(1-1/16) ...................3
for Li2+ , E = 13.6(1/n12 - 1/n22)*9 (Z = 3 )
this energy is equal to energy from in 3
13.6(1-1/16) = 13.6*9(1/n12 - 1/n22)
1/9 - 1/9*16 = 1/32 - 1/122 = 1/n12 - 1/n22
n1 = 3 , n2 = 12
final exited state = n = 12
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