$${1 \over \lambda } = {R_H}{Z^2}\left[ {{1 \over {n_1^2}} - {1 \over {n_2^2}}} \right]$$

For singly-ionized helium atom, Z = 2. For hydrogen atom Z = 1.

For Balmer series n₁ = 2.

For first spectral line of hydrogen :

$${1 \over {6561}} = {R_H} \times {(1)^2}\left[ {{1 \over {{2^2}}} - {1 \over {{3^2}}}} \right] = {{5R} \over {36}}$$

$$ \Rightarrow {R_H} = {{36} \over {5 \times 6561}}$$

For second spectral line of helium,

$${1 \over \lambda } = {R_H} \times {(2)^2}\left[ {{1 \over {{2^2}}} - {1 \over {{4^2}}}} \right] = {{3{R_H}} \over 4}$$

$$ = {3 \over 4} \times {{36} \over {5 \times 6561}}$$

$$ \Rightarrow \lambda = 1215\,\mathop A\limits^o $$