The speed of a proton is c / 20. What will be | vedclass

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(D) The de Broglie wavelength $\lambda$ is given by the formula $\lambda = \frac{h}{p} = \frac{h}{mv}$.Given, velocity $v = \frac{c}{20}$, where $c =

Vedclass · Accepted Answer

$2.64 	imes 10^{-14} 	ext{ m}$

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(D) The de Broglie wavelength $\lambda$ is given by the formula $\lambda = \frac{h}{p} = \frac{h}{mv}$.Given, velocity $v = \frac{c}{20}$, where $c = 3 	imes 10^8 	ext{ m/s}$.Mass of a proton $m_p \approx 1.67 	imes 10^{-27} 	ext{ kg}$.Planck's constant $h = 6.63 	imes 10^{-34} 	ext{ J} \cdot 	ext{s}$.Substituting the values:$\lambda = \frac{6.63 	imes 10^{-34}}{1.67 	imes 10^{-27} 	imes (3 	imes 10^8 / 20)}$$\lambda = \frac{6.63 	imes 10^{-34} 	imes 20}{1.67 	imes 10^{-27} 	imes 3 	imes 10^8}$$\lambda = \frac{132.6 	imes 10^{-34}}{5.01 	imes 10^{-19}}$$\lambda \approx 26.46 	imes 10^{-15} 	ext{ m} = 2.646 	imes 10^{-14} 	ext{ m}$.Thus, the correct option is $D$.

The speed of a proton is $c / 20$. What will be the de Broglie wavelength associated with it?

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