Answer
$\lambda_2 = 1.58\times 10^{-6}~m$
Work Step by Step
The effect of scattering is proportional to $\frac{1}{\lambda^4}$
We can find the wavelength $\lambda_2$ such that the scattering is only $1\%$:
$\frac{\lambda_2^4}{\lambda_1^4} = \frac{1}{1/100}$
$\lambda_2^4 = 100~\lambda_1^4$
$\lambda_2 = \sqrt[4] {100}~\lambda_1$
$\lambda_2 = (\sqrt[4] {100})~(500\times 10^{-9}~m)$
$\lambda_2 = 1.58\times 10^{-6}~m$
