A nucleus \(A\), with a finite de -broglie wavelength \(\lambda_A\), undergoes spontaneous fission into two nuclei \(B\) and \(C\) of equal mass. \(B\) flies in the same direction as that of \(A\), while \(C\) flies in the opposite direction with a velocity equal to half of that of \(B\). The de -Broglie wavelength \(\lambda_B\) and \(\lambda_C\) of \(B\) and \(C\) are respectively

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(D) \(\frac{\lambda_A}{2}\), \(\lambda_A\)

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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 \(\lambda=\frac{h}{p}\)

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

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