In order to coincide the parabolas formed by singly ionized 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 thses

Answer

C

Explanation

Using `Z^(2) = k((q)/(m)) y` , where `k = (B^(2) LD)/(E )`
For parabolas to coincide in the two photographs , the
`(kq)/(m)` should be same for the two cases . Thus ,
`(B_(1) ^(2) LD e)/(E_(1) m_(1)) = (B_(2)^(2) LD ( 2e))/( E_(2) m_(2))`
` rArr (m_(1))/(m_(2)) = ((B_(1))/(B_(2)))^(2) xx ((E_(2))/(E_(1))) xx (1)/(2) = (9)/(4) xx (2)/(1) xx (1)/(2) = (9)/(4)`