A beam consisting of four types of ions A, B, C and D enters a region at P that contains a uniform magnetic field as shown in fig. The field is perpendicular to the plane of the paper, but its precise direction is not given. All ions in the beam travel with the same speed. The table on the next page shows the masses and charges of the ions
Ion
Mass
Charge
A
2m
e
B
4m
-e
C
2m
-e
D
m
+e
The ions falls at different positions 1, 2, 3 and 4 as shown. Correctly match the ions with their respective position of fall

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Solution

We know that $r = m v / q B$ . So, larger the mass, larger is the radius. Since radius of path '4' is largest, so path '4' should correspond to ion B.
Hence, $i i \to a$ .
Now path '2' should correspond to ion C, because charge on both B and C is negative, so their paths should be on the same side.
Hence, $i i i . \to b$ .
Now, radii of path '2' and '3' are same. If path '2' corresponds to C, then path '3' should correspond to ion A, because masses of A and C are same.
Hence, $i, \to d$ .
Now, remaining path '1' should correspond to D.
Hence, $i v . \to c$ .

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