Question

29. The atomic spectrum of Li2* ion arises due to the transition of an electron from n,1 to n2. If n,1 + n 2 = 4 and (n,2 - n,1) = 2. Find the wavelength of this line in Li* ion
(A) 1.14 nm (B) 11.4 nm (C) 114 nm (D) 1140 nn​

Answer 1

Explanation:

Calculation of value of n1 and n2

According to available information,

n1+n2=4 and n2−n1=2

On adding , 2n2=6 or n2=3 and n1=4−3=1.

Step II. Calculation of wavelength of transition

According to Rydberg formula,

1λ=v¯=RHZ2(1n21−1n22),RH=109678cm−1,Z(Li2+)=3,n1=1,n2=3

∴ 1λ=(109678cm−1)×(3)2(112−132)=(109678cm−1)×9×89=877424cm−1

λ=1(877424cm−1)=(1.14×10−6cm)=1.14×10−6×110−7=11.4nm. (∴1nm=10−7cm)