An electron of mass m_{e} and a proton of mas | vedclass

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(B) The de-Broglie wavelength $\lambda$ is given by the formula: $\lambda = \frac{h}{mv}$,where $h$ is Planck's constant,$m$ is the mass,and $v$ is th

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$1836$

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(B) The de-Broglie wavelength $\lambda$ is given by the formula: $\lambda = \frac{h}{mv}$,where $h$ is Planck's constant,$m$ is the mass,and $v$ is the speed.For an electron,the wavelength is $\lambda_{e} = \frac{h}{m_{e}v}$.For a proton,the wavelength is $\lambda_{p} = \frac{h}{m_{p}v}$.Taking the ratio of the two wavelengths:$\frac{\lambda_{e}}{\lambda_{p}} = \frac{h / m_{e}v}{h / m_{p}v} = \frac{m_{p}}{m_{e}}$.Given that the mass of a proton $m_{p} \approx 1.67 	imes 10^{-27} \ kg$ and the mass of an electron $m_{e} \approx 9.11 	imes 10^{-31} \ kg$,the ratio is:$\frac{\lambda_{e}}{\lambda_{p}} = \frac{1.67 	imes 10^{-27}}{9.11 	imes 10^{-31}} \approx 1833 \approx 1836$ (using standard mass ratios).Thus,the ratio $\lambda_{e} / \lambda_{p} = 1836$.

An electron of mass $m_{e}$ and a proton of mass $m_{p}$ are moving with the same speed. The ratio of their de-Broglie's wavelengths $\lambda_{e} / \lambda_{p}$ is

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