Question

The velocity of particle $A$ is $0.1 \,ms ^{-1}$ and that of particle $B$ is $0.05 \,ms ^{-1}$. 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, $v _A=0.1 \,ms ^{-1}$ and $v _B=0.05\, ms ^{-1}$
also, $m_B=5\, m_A$ de-Broglie wavelength, $\lambda=\frac{h}{m v }$
$\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} $
$=\frac{5 m_A \times 0.05}{m_A \times 0.1}=5 \times 0.5=2.5=5 / 2$
$\therefore \lambda_{ A }: \lambda_{ B }=5: 2$