Given that
Total energy of two rays 2E = 10.2 BeV
2E = 10.2 * 10^9 eV
2E = 10.2 * 10^9 * 1.6*10^{-10} J
Energy of ray E = \frac{10.2 * 10^9 * 1.6*10^{-10}}{2} J
E = 8.16 *10^{-10} J
Step 1: Finding the wavelength of y-rays
Energy of proton E=h\upsilon\ =\ \frac{hc}{\lambda}
Where, h - Planck's constant( 6.63*10^{-34} Js}), speed of light c = 3*10^{8} m/s and \upsilon - frequency.
\lambda = \frac{h c}{ E }
\lambda = \frac{(6.63*10^{-34})*(3* 10^{8})}{8.16 *10^{-10}}
\lambda = 2.436 * 10^{-16} m
Therefore, wavelength of y-rays \lambda = 2.436 * 10^{-16} m