Note :

(1)   In Lyman Series, transition happens in n = 1 state
from n = 2, 3, . . . . . $$ \propto $$

(2)   In Balmer Series, transition happens in n = 2 state
from n = 3, 4, . . . . . $$ \propto $$

(3)   In Paschen Series, transition happens in n = 3 state
from n = 4, 5, . . . . . $$ \propto $$

(4)   In Bracktt Series, transition happens in n = 4 state
from n = 5, 6 . . . . . . $$ \propto $$

(5)   In Pfund Series, transition happens in n = 5 state
from n = 6, 7, . . . . $$ \propto $$

We know,

     $${1 \over \lambda }$$ = Rz² ($${1 \over {n_1^2}}$$ $$-$$ $${1 \over {n_2^2}}$$)

The shortest wavelength of hydrogen atom in Lyman series is from n₁ = 1 to n₂ = $$ \propto $$

$$\therefore\,\,\,$$ $${1 \over A}$$ = 1² R ($${1 \over {{1^2}}}$$ $$-$$ $${1 \over {{ \propto ^2}}}$$)    [for hydrogen, z = 1]

$$ \Rightarrow $$ $$\,\,\,$$ $${1 \over A}$$ = R

The longest wavelength in pascal series of He⁺ is from n₁ = 3 to n₂ = 4

For He⁺, z = 2.

$${1 \over \lambda }$$ = RZ² ($${1 \over {n_1^2}}$$ $$-$$ $${1 \over {n_2^2}}$$)

$$ \Rightarrow $$$$\,\,\,$$ $${1 \over \lambda }$$ = $${1 \over A}$$ (2)² ($${1 \over {{3^2}}}$$ $$-$$ $${1 \over {{4^2}}}$$)

$$ \Rightarrow $$$$\,\,\,$$ $${1 \over \lambda }$$ = $${4 \over A}$$ $$\left( {{7 \over {16 \times 9}}} \right)$$ = $${7 \over {36A}}$$

$$ \Rightarrow $$$$\,\,\,$$ $$\lambda $$ = $${{36A} \over 7}$$