Question

A nucleus A, with a finite de-broglie wavelength ${\lambda }_A$, undergoes spontaneous fission into to 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 wavelengths ${\lambda }_B$ and ${\lambda }_C$ of B and C are respectively : -

• A. $2{\lambda }_A,{\lambda }_A$
• B. ${\lambda }_A,2{\lambda }_A$
• C. ${\lambda }_A,\frac{{\lambda }_A}{2}$
• D. $\frac{{\lambda }_A}{2},{\lambda }_A$

Answer 1

Answer: (D)

let mass of $B$ and $C$ is $m$ each.
By momentum conservation
$2m{v}_0=mv-\frac{mv}{2}$
$v=4v_0$
$p_A=2m{v}_0{p}_B=4m{v}_0{p}_c=2m{v}_0$
De-Broglie wavelength $\lambda =\frac{h}{p}$
${\lambda }_A=\frac{h}{2m{v}_0};{\lambda }_B=\frac{h}{4m{v}_0};{\lambda }_C=\frac{h}{2m{v}_0}$