Q. The de Broglie wavelength of a proton and α-particle are equal. The ratio of their velocities is:

     (1) 4:2                        (2) 4:1                        (3) 1:4                          (4) 4:3

 

 

Ans. (2)

Explanation:

From De-Broglie’s concept,

straight lambda space equals space straight h over mv
straight lambda subscript straight P space equals space straight lambda subscript straight alpha
therefore space straight v space straight alpha 1 over straight m
straight v subscript straight P over straight v subscript straight alpha space equals space straight m subscript straight alpha over straight m subscript straight P space equals space fraction numerator 4 straight m subscript straight P over denominator straight m subscript straight P end fraction space equals 4 over 1