`alpha`-particle and deuteron moves with speed v and 2v respectively .What will be ratio of de-Broglie wavelength ?

Options

A. `1:1`
B. `sqrt(2):1`
C. `1:sqrt(2)`
D. `2:1`

Answer

A

Explanation

In `lambda=(h)/(mv)`,h is constant
`therefore lambda prop (1)/(mv)`
`therefore (lambda_(1))/(lmbda_(d))=(m_(d)v_(d))/(m_(alpha)v_(alpha))`
`=(2m_(p))/(4m_(p))xx(2v)/(v)=(4m_(p)v)/(4m_(p)v)=(1)/(1)`