The velocity of particle $\mathrm{A}$ is $0.1 \mathrm{~ms}^{-1}$ and that of particle $\mathrm{B}$ is $0.05…

The velocity of particle $\mathrm{A}$ is $0.1 \mathrm{~ms}^{-1}$ and that of particle $\mathrm{B}$ is $0.05 \mathrm{~ms}^{-1} .$ If the mass of particle $\mathrm{B}$ is five times that of particle $\mathrm{A}$, then the ratio of deBroglie wavelengths associated with the particles $\mathrm{A}$ and $\mathrm{B}$ is
  1. $2: 5$
  2. $3: 4$
  3. $6: 4$
  4. $5: 2$

Solution

Given, $\mathrm{v}_{\mathrm{A}}=0.1 \mathrm{~ms}^{-1}$ and $\mathrm{v}_{\mathrm{B}}=0.05 \mathrm{~ms}^{-1}$ also,
$\mathrm{m}_{\mathrm{B}}=5 \mathrm{~m}_{\mathrm{A}}$
de-Broglie wavelength, $\lambda=\frac{\mathrm{h}}{\mathrm{mv}}$
$\therefore \frac{\lambda_{\mathrm{A}}}{\lambda_{\mathrm{B}}}=\frac{\mathrm{h} / \mathrm{m}_{\mathrm{A}} \mathrm{v}_{\mathrm{A}}}{\mathrm{h} / \mathrm{m}_{\mathrm{B}} \mathrm{V}_{\mathrm{B}}}=\frac{\mathrm{m}_{\mathrm{B}} \mathrm{V}_{\mathrm{B}}}{\mathrm{m}_{\mathrm{A}} \mathrm{v}_{\mathrm{A}}}$
$=\frac{5 \mathrm{~m}_{\mathrm{A}} \times 0.05}{\mathrm{~m}_{\mathrm{A}} \times 0.1}=5 \times 0.5=2.5=5 / 2$
$\therefore \lambda_{\mathrm{A}}: \lambda_{\mathrm{B}}=5: 2$ .

Asked in: JEE-TOPICTESTS-CHEMISTRY

Practice more STRUCTURE OF ATOM questions on Aicharya