The orbital angular momentum is

$$L = {{nh} \over {2\pi }}$$

$${{3h} \over {2\pi }} = {{nh} \over {2\pi }} \Rightarrow n = 3$$

The radius of the orbit is

$$4.5({a_0}) = {a_0}\left( {{{{n^2}} \over Z}} \right)$$

$$Z = {{{n^2}} \over {4.5}} = {{{3^2}} \over {4.5}} = {9 \over {4.5}} = 2$$

Thus, the possible transitions are 3$$\to$$2, 3$$\to$$1 and 2$$\to$$1. For the transition 3$$\to$$2, the wavelength is

$${1 \over \lambda } = R{(2)^2}\left[ {{1 \over 4} - {1 \over 9}} \right] = 4R\left[ {{{9 - 4} \over {36}}} \right] = {{5R} \over 9}$$

$$ \Rightarrow \lambda = {9 \over {5R}}$$

For the transition 3$$\to$$1, the wavelength is

$${1 \over \lambda } = R{(2)^2}\left[ {1 - {1 \over 9}} \right] = 4R\left( {{8 \over 9}} \right) = {{32R} \over 9}$$

$$ \Rightarrow \lambda = {9 \over {32R}}$$

For the transition 2$$\to$$1, the wavelength is

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

$$ \Rightarrow \lambda = {1 \over {3R}}$$