Question

The velocity of particle $A$ is $0.1m{s}^{-1}$ and that of particle $B$ is $0.05m{s}^{-1}$. If the mass of particle $B$ is five times that of particle $A$, then the ratio of de-Broglie wavelengths associated with the particles $A$ and $B$ is

• A. $2:5$
• B. $3:4$
• C. $6:4$
• D. $5:2$

Answer 1

Answer: (D)

Given, $v_A=0.1m{s}^{-1}$ and $v_B=0.05m{s}^{-1}$
also, $m_B=5m_A$ de-Broglie wavelength, $\lambda =\frac{h}{mv}$
$\therefore \frac{{\lambda }_A}{{\lambda }_B}=\frac{h/m_A{v}_A}{h/m_B{v}_B}=\frac{m_B{v}_B}{m_A{v}_A}$
$=\frac{5m_A\times 0.05}{m_A\times 0.1}=5\times 0.5=2.5=5/2$
$\therefore {\lambda }_A:{\lambda }_B=5:2$