Which of the following represents the wavelength of spectral line of Balmer series of {He}^{+}ion? ( R = {Rydberg constant,}\ n > 2) [AP EAPCET 24 May 2025 S1]

Correct Answer is : n2R(n−2)(n+2)\;\;n²/R(n-2)(n+2)R(n−2)(n+2)n2

Correct Answer is : n2R(n−2)(n+2)\;\;n²/R(n-2)(n+2)R(n−2)(n+2)n2

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Atomic Structure

Section: Chemistry

Question : 2 of 32

Marks: +1, -0

\mathrm{He}^{+}

( R = \text{Rydberg constant,}\ n > 2)

Solution:

Using Rydberg formula

\;\frac{1}{\lambda}=R z^2 \left[ \;\frac{1}{n_f^2} - \;\frac{1}{n_i^2} \right]

for

\mathrm{He}^{+}, z=2

, for Balmer series,

n_f=2

The initial energy level,

n_i=n

where

n>2

\;\frac{1}{\lambda}\;=R(2)^2 \left[ \;\frac{1}{2^2} - \;\frac{1}{n^2} \right]

\Rightarrow \;\; \;\frac{1}{\lambda}\;=4 R \left( \;\frac{1}{4} - \;\frac{1}{n^2} \right)

On simplifying above equation

\lambda\;=\;\frac{n^2}{R (n^2-4)}

\Rightarrow \;\; \lambda\;=\;\frac{n^2}{R(n-2)(n+2)}

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