Magnetic Effects Of Current Question 399
Question: In a mass spectrometer used for measuring the masses of ions, the ions are initially accelerated by an electric potential V and then made to describe semicircular path of radius R using a magnetic field B. If V and B are kept constant, the $ ratio,( \frac{charge,on,the,ion}{mass,of,the,ion} ) $ will be proportional to
Options:
A) $ 1/R^{2} $
B) $ R^{2} $
C) R
D) $ 1/R $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] In mass spectrometer, when ions are accelerated through potential V $ \frac{1}{2}mv^{2}=qV $ ??.(i) As the magnetic field curves the path of the ions in a semicircular orbit $ Bqv=\frac{mv^{2}}{R}\Rightarrow v=\frac{BqR}{m} $ ??..(ii) Substituting (ii) in (i) $ \frac{1}{2}m{{[ \frac{BqR}{m} ]}^{2}}=qV $ or $ \frac{q}{m}=\frac{2V}{B^{2}R^{2}} $ Since F and B are constants,
$ \therefore \frac{q}{m}\propto \frac{1}{R^{2}} $
BETA
