A particle is moving 5 times as fast as an el | vedclass

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(D) Let the mass of the particle be $m$ and the mass of the electron be $m_e = 9.1 	imes 10^{-31} \ kg$.Let the speed of the electron be $v_e = V$.Th

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$9.7 	imes 10^{-28} \ kg$

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(D) Let the mass of the particle be $m$ and the mass of the electron be $m_e = 9.1 	imes 10^{-31} \ kg$.Let the speed of the electron be $v_e = V$.Then,the speed of the particle is $v_p = 5V$.The de-Broglie wavelength is given by $\lambda = \frac{h}{mv}$.For the particle: $\lambda_p = \frac{h}{m(5V)}$.For the electron: $\lambda_e = \frac{h}{m_e V}$.The ratio of the wavelengths is $\frac{\lambda_p}{\lambda_e} = \frac{h}{5mV} 	imes \frac{m_e V}{h} = \frac{m_e}{5m}$.Given $\frac{\lambda_p}{\lambda_e} = 1.878 	imes 10^{-4}$,we have $\frac{m_e}{5m} = 1.878 	imes 10^{-4}$.Solving for $m$: $m = \frac{m_e}{5 	imes 1.878 	imes 10^{-4}} = \frac{9.1 	imes 10^{-31}}{9.39 	imes 10^{-4}} \approx 9.7 	imes 10^{-28} \ kg$.

$A$ particle is moving $5$ times as fast as an electron. The ratio of the de-Broglie wavelength of the particle to that of the electron is $1.878 \times 10^{-4}$. The mass of the particle is close to

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