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For an electron to have the same de Broglie wave length as that of a Deuteron, its velocity should be __ times that of Deuteron

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1/1836

1/3672

1836

3672

answer is C.

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Detailed Solution

The Debroglie's wave length $λ = \frac{h}{mv}$

$λ = \frac{h}{m_{e} v_{e}} e = electron λ = \frac{h}{m_{D} v_{D}} D = deutron$

$\frac{h}{m_{e} v_{e}} = \frac{h}{m_{D} v_{D}} \frac{v_{e}}{v_{D}} = \frac{m_{D}}{m_{e}} \frac{v_{e}}{v_{D}} = \frac{2 m_{H}}{\frac{1}{1836} m_{H}} \frac{v_{e}}{v_{D}} = 3672$

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