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 :

Explanation

de -Broglie wavelength `(lamda)` is given by `K=qV`
`lamda=h/p=h/(sqrt(2mK))=h/(sqrt(2mqV))" " ( :. p=sqrt(2mK))`
Substituting the values we get
`:.(lamda_(A))/(lamda_(B))=(sqrt(2m_(B)q_(B)V_(B)))/(sqrt(2m_(A)q_(A)V_(A)))=sqrt((4m.q.2500)/(m.z.50))`
`=2sqrt(50)=2xx7.07=14.14`