A) 1 : 3
B) 2 : 4
C) 3 : 1
D) 4 : 2
Correct Answer: A
Solution :
[a] For same magnetic field \[\frac{{{y}^{2}}}{x}\propto \frac{1}{E}\left( \frac{e}{m} \right)\] For singly ionized particle, \[\frac{{{y}^{2}}}{x}\propto \frac{1}{{{E}_{1}}}\frac{e}{{{m}_{1}}}\] For doubly ionised particle, \[\frac{{{y}^{2}}}{x}\propto \frac{1}{{{E}_{2}}}\frac{2e}{{{m}_{2}}}\] Since the parabolas for both the particles are identical, \[\frac{1}{{{E}_{1}}}\frac{e}{{{m}_{1}}}=\frac{1}{{{E}_{2}}}\frac{2e}{{{m}_{2}}}\] So \[\frac{{{m}_{1}}}{{{m}_{2}}}=\frac{{{E}_{2}}}{2{{E}_{1}}}=\frac{2000}{2\times 3000}=\frac{1}{3}\]
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