Question

After absorbring a slowly moving neutron of Mass mN (momentum $\approx$ 0) a nucleus of mass M breaks into two nuclei of masses $m_1$ and $5m_1$ ($6\, m_1 = M + mN$ ) respectively. If the de Broglic wavelength of the nucleus with mass $m_1$ is $\lambda$, the de Broglie wevelength of the nucleus will be:

• A. $5\,\lambda$
• B. $\lambda $\5
• C. $\lambda$
• D. $25\,\lambda$

Answer 1

Answer: (C)

$P_i = 0$
$P_f = P_1 + P_2$
$P_i = P_f$
$0 = P_1 + P_2$
$(P_1 = -P_2)$
$\lambda_{1} = \frac{h}{P_{1}}$
$\lambda _{2} = \frac{h}{P_{2}}$
$\left|\lambda_{1}\right| = \left|\lambda_{2}\right|$
$\lambda _{1} = \lambda _{2} = \lambda.$