The energy ($E$) of a photon or radiation is inversely proportional to its wavelength ($\lambda$) according to the Planck-Einstein relation: $E = \frac{hc}{\lambda}$ where $h$ is Planck's constant and $c$ is the speed of light.

Since $hc$ is constant, we can write the ratio: $\frac{E_1}{E_2} = \frac{\lambda_2}{\lambda_1}$

Given: $E_1 = 25 \text{ eV}$ $E_2 = 50 \text{ eV}$

Calculation: $\frac{25}{50} = \frac{\lambda_2}{\lambda_1}$ $\frac{1}{2} = \frac{\lambda_2}{\lambda_1}$ $\lambda_1 = 2\lambda_2$

Thus, the wavelength of the first radiation is twice that of the second.