A nucleus A with a finite de-broglie wavelength


A nucleus $A$, with a finite de-broglie wavelength $\lambda_{A}$, undergoes spontaneous fission into two nuclei $\mathrm{B}$ and $\mathrm{C}$ 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 $\mathrm{B}$. the de-Broglie wavelengths $\lambda_{\mathrm{B}}$ and $\lambda_{\mathrm{C}}$ of $\mathrm{B}$ and $\mathrm{C}$ are respectively :

  1. (1) $\lambda_{\mathrm{A}}, 2 \lambda_{\mathrm{A}}$

  2. (2) $2 \lambda_{A}, \lambda_{A}$

  3. (3) $\lambda_{A}, \frac{\lambda_{A}}{2}$

  4. (4) $\frac{\lambda_{\mathrm{A}}}{2}, \lambda_{\mathrm{A}}$

Correct Option: , 4


(4) $\quad \vec{P}=\vec{P}+\vec{P}_{2}$

or $\vec{P}=\overrightarrow{P^{\prime}}-\frac{\overrightarrow{P^{\prime}}}{2}$


As $\lambda=\frac{h}{P}$

$\Rightarrow \lambda_{B}=\frac{\lambda_{A}}{2}$ and $\lambda_{\mathrm{C}}=\lambda_{\mathrm{A}}$

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