Question

For hydrogen atom, $\lambda_1$ and $\lambda_2$ are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in figure The ratio of $\lambda_1$ and $\lambda_2$ is $\frac{x}{32}$ The value of $x$ is

Answer 1

The correct answer is 27.
λ1​=Rz2[n12​1​−n22​1​]
λ1​1​=Rz2[121​−321​]=98​Rz2.....(1)
λ2​1​=Rz2[121​−221​]=43​Rz2......(2)
1/2⇒λ1​λ2​​=98​×34​=2732​
λ2​λ1​​=3227​
=27