Dual Nature Of Light Question 114
Question: In order to coincide the parabolas formed by singly ionised ions in one spectrograph and doubly ionized ions in the other Thomson?s mass spectrograph, the electric fields and magnetic fields are kept in the ratios 1 : 2 and 3 : 2 respectively. Then the ratio of masses of the ions is
Options:
A) 3 : 4
B) 1 : 3
C) 9 : 4
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Using $ Z^{2}=k( \frac{q}{m} )y; $ where $ k=\frac{B^{2}LD}{E} $ . For parabolas to coincide in the two photographs, the $ \frac{k,q}{m} $ should be same for the two cases. Thus, $ \frac{B_{1}^{2}\ LDe}{E_{1}m_{1}}=\frac{B_{2}^{2}LD,(2e)}{E_{2}m_{2}} $
Þ $ \frac{m_{1}}{m_{2}}={{( \frac{B_{1}}{B_{2}} )}^{2}}\times ( \frac{E_{2}}{E_{1}} )\times \frac{1}{2} $ $ =\frac{9}{4}\times \frac{2}{1}\times \frac{1}{2}=\frac{9}{4} $
BETA
