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A particle A of mass ‘m’ and charge ‘q’ ...

A particle A of mass ‘m’ and charge ‘q’ is accelerated by a potential difference of 50 V. Another particle B of mass ‘4 m’ and charge ‘q’ is accelerated by a potential difference of 2500 V. The ratio of de-Broglie wavelengths `(lambda_A)/(lambda_B)` is close to :

A

14.14

B

0.07

C

10

D

4.47

Text Solution

Verified by Experts

The correct Answer is:
A
`P^2=2km`
`P^2//2m=k=qv`
`P=sqrt(2mqv), lambda=(h)/(P)`
`lambda=(h)/(sqrt(2mqv)),lambda_(A)=(h)/(sqrt(2xx mq xx 50))`
`lambda_(B)=(h)/(sqrt(2xx4m xxqxx250)) rArr lambda_(A)/(lambda_(B))=sqrt(2xx4m xxqxx2500)/(sqrt(2xxmxxqxx50))`
`lambda_(A)/lambda_(B)=sqrt((2xx 4m xx q xx2500)/(2 xx m xxq xx 50))=14.14`
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