d
Let mass of \(B\) and \(C\) is \(m\) each. By momentum conservation \(2 m v_{0}=m v-\frac{m v}{2}\)

\(\mathrm{v}=4 \mathrm{v}_{0}\)

\({{\text{P}}_{\text{A}}} = 2{\text{m}}{{\text{v}}_0}\) \({{\text{p}}_{\text{B}}} = 4{\text{m}}{{\text{v}}_0}\) \({{\text{p}}_{\text{c}}} = 2{\text{m}}{{\text{v}}_0}\)

De-Broglie wavelength \(\lambda=\frac{h}{p}\)

\(\lambda_{\mathrm{A}}=\frac{\mathrm{h}}{2 \mathrm{mv}_{0}}\) ; \(\lambda_{\mathrm{B}}=\frac{\mathrm{h}}{4 \mathrm{mv}_{0}}\) ; \(\lambda_{\mathrm{C}}=\frac{\mathrm{h}}{2 \mathrm{mv}_{0}}\)