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Q.

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

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a

1836

b

1/1836

c

3672

d

1/3672

answer is C.

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Detailed Solution

The mass of hydrogen is 1836 times greater than the mass of electron. The mass of deuteron (D12) is two times than the mass of hydrogen. Therefore, the velocity of electron is 3672 times than the velocity of Deuteron.

De-Broglie wave equation is

λ=hmv

For electron,

λ=hmeveve=hλme  

For Deuteron,

λ=hmDvDvD=hλmD

As me=11836×2of mD, then the velocity of electron is 3672 times than the velocity of Deuteron.

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