Q.) Which transition of Li2+ is associated with same energy change as n=6 to n=4 transition in He+.

(I) n=3 to n=1 (II) n=8 to n=6 ( III) n=9 to n=6 (IV) n=2 to n=1

Formula for Energy change for transition of Hydrogen-like species is as follows:

ΔE = 2.18×10-18Z2(1n12-1n22)where Z is atomic number, n1 and n2 are lower and final transition states. For He+ the energy change isΔE =- 2.18×10-18(2)2(142-162)= -2.18×10-18(536) JFor Li2+ the energy change for (i) n = 3 to n=1ΔE = -2.18×10-18(3)2(112-132)= 2.18×10-18(8) J(ii) n = 8 to n = 6ΔE =- 2.18×10-18(3)2(162-182)=- 2.18×10-18(764) J(iii) n = 9 to n=6ΔE =- 2.18×10-18(3)2(162-192)= -2.18×10-18(536) J(iv) n = 2 to n =1ΔE =- 2.18×10-18(3)2(112-142)=- 2.18×10-18(13516) J 

So, the energy change in third part is same as of the He+ ion fro transition n = 6 to n =4.
Correct option is (iii).

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