1. Use the photon energy relation

For a transition between two energy levels,

$E = h\nu = \frac{hc}{\lambda}$

So wavelength is inversely proportional to the energy gap:

$\lambda \propto \frac{1}{\Delta E}$

Hence,

$\frac{\lambda_1}{\lambda_2} = \frac{\Delta E_2}{\Delta E_1}$

2. Read the energy gaps from the level diagram

From the given figure, the two marked transitions correspond to energy differences in the ratio

$\Delta E_1 : \Delta E_2 = 3:4$

Therefore,

$\frac{\lambda_1}{\lambda_2} = \frac{\Delta E_2}{\Delta E_1} = \frac{4}{3}$

3. Match with the options

Thus,

$r = \frac{\lambda_1}{\lambda_2} = \frac{4}{3}$

So the correct option is:

B: $\frac{4}{3}$

4. Comparison with stored answer

The stored correct answer is A: $\frac{1}{3}$, but from the energy-gap relation and the level differences, the ratio comes out to be

$\boxed{\frac{4}{3}}$

So I do not agree with the stored answer.