A nucleus A, with a finite de -broglie wavelength _A, undergoes s… - Vidyadip

MCQ

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

A
$\lambda_A$, $2\lambda_A$
B
$2\lambda_A$, $\lambda_A$
C
$\lambda_A$, $\frac{\lambda_A}{2}$
✓
$\frac{\lambda_A}{2}$, $\lambda_A$

✓

Answer

Correct option: D.

$\frac{\lambda_A}{2}$, $\lambda_A$

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 $\lambda=\frac{h}{p}$

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

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