Em Waves Question 73
Question: The ratio of de Broglie wavelength of a a-particle to that of a proton being subjected to the same magnetic field so that the radii of their paths are equal to each other assuming the field induction vector $ \vec{B} $ is perpendicular to the velocity vectors of the a-particle and the proton is
Options:
A) 1
B) $ \frac{1}{4} $
C) $ \frac{1}{2} $
D) $ 2 $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] When a charged particle (charge q, mass m) enters perpendicularly in a magnetic field [b] then, radius of the path $ r=\frac{mv}{qB}\Rightarrow mv=q\beta r. $ Also de Broglie wavelength, $ \lambda =\frac{h}{mv} $
$ \Rightarrow \lambda =\frac{h}{qBr}\Rightarrow \frac{{\lambda _{\alpha }}}{{\lambda _{p}}}=\frac{q _{p}r _{p}}{{q _{\alpha }}{r _{\alpha }}}=\frac{1}{2} $
BETA
