Two fast moving particles $X$ and $Y$ are associated with de Broglie wavelengths $1 \mathrm{~nm}$ and $4 \mathrm{~nm}$ respectively. If mass of $X$ is nine times the mass of $Y$, the ratio of kinetic energies of $X$ and $Y$ would be

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Aicharya · Accepted Answer

de Broglie wavelength $\lambda=\frac{h}{m v}$
$\frac{\lambda_{1}}{\lambda_{2}}=\frac{m_{2} v_{2}}{m_{1} v_{1}} ; \frac{1}{4}=\frac{1}{9} \times \frac{v_{2}}{v_{1}}$
$\frac{v_{2}}{v_{1}}=\frac{9}{4} ; \frac{v_{1}}{v_{2}}=\frac{4}{9}$
$\mathrm{KE}=\frac{1}{2} m v^{2}$
$\frac{K E_{1}}{K E_{2}}=\frac{m_{1}}{m_{2}} \times \frac{v_{1}^{2}}{v_{2}^{2}}=\frac{9}{1} \times\left(\frac{4}{9}ight)^{2}=\frac{16}{9}$

Two fast moving particles $X$ and $Y$ are associated with de Broglie wavelengths $1 \mathrm{~nm}$ and $4…

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