Solution:
Solution
$$n_2+n_1=4$$......(1)
$$n_2^2-n^2_1=8$$
$$\Rightarrow (n_2+n_1)(n_2-n_1)=8$$
$$\Rightarrow n_2-n_1=2$$.......(2)
From 1 and 2
$$n_1=3,n_2=1$$
$$E=-13.6(\dfrac{1}{n_1}-\dfrac{1}{n_2})$$
$$=-13.6(\dfrac{1}{9}-1)$$
$$=\dfrac{8}{9}\times 13.6$$
$$\bar{v}=R_HZ^2(\dfrac{1}{h^2_1}-\dfrac{1}{h_2})$$
$$\Rightarrow \dfrac{1}{\lambda}==R_H\times 4\times \dfrac{8}{9} $$
$$\Rightarrow =\lambda=\dfrac{9}{32}R_H$$