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Velocity of a proton is $c / 20$ (c is velocity of light). de – Broglie wavelength associated with its motion is ______ (Neglect relativistic mass correction)

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$2.64 \times 10^{- 14} \overset{o}{A}$

$2.64 \times 10^{- 24} mm$

$2.64 \times 10^{- 24} cm$

$2.64 \times 10^{- 14} m$

answer is D.

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Detailed Solution

$λ = \frac{h}{mv}$

$∵ v = \frac{c}{20} = \frac{3 \times 10^{8}}{20} 1.5 \times 10^{7} m / sec$

$h = 6.626 \times 10^{- 34} J - s, m = 1.67 \times 10^{- 27} kg$

$∴ λ = \frac{6.626 \times 10^{- 34}}{1.67 \times 10^{- 27} \times 1.5 \times 10^{7}}$

$\Rightarrow λ = 2.64 \times 10^{- 14} m$

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