Dual Nature Of Light Question 109
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 path are equal to each other assuming the field induction vector $ \overrightarrow{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:
When a charged particle (charge q, mass m) enters perpendicularly in a magnetic field than, radius of the path described by it $ r=\frac{mv}{qB}\Rightarrow mv=qBr $ . Also de-Broglie wavelength $ \lambda =\frac{h}{mv} $
Þ $ \lambda =\frac{h}{qBr} $
$ \Rightarrow \frac{{\lambda_{\alpha }}}{{\lambda_{p}}}=\frac{q_{p}r_{p}}{{q_{\alpha }}{r_{\alpha }}}=\frac{1}{2} $
BETA
