Question

In hydrogen-like atom (z = 11), nth line of lyman series has wavelength equal to the de-broglies wavelength of electron in the level from which it originated. What is the value of n?

Answer 1

 1λ=Rz2(1n21−1n22)

        1λ=R(11)2(11−1n2)

        λ=hρ=hmv

        λ=hrmvr=rh2πnh=2πrn.

        λ=2πrn=(π(0.529×10−10)n2)(n)(11)

        1λ=112π(0.529×10−10)n=11(2π)(0.529×10−10)n=1.1×107(11)2(1−1n2)

         =12π(0.529×10−10)(1.1×102)(11)=n−1n

         n−1n=25

         n2−1=25 n

         n2−25 n−1=0

          n=25

         Hence answer = 24