A proton, a deuteron and an particle with the same KE enter in a region of uniform magnetic field, moving at right angles to magnetic field. What is the ratio of the radii of their circular paths?

Question

A proton, a deuteron and an $α$ particle with the same KE enter in a region of uniform magnetic field, moving at right angles to magnetic field. What is the ratio of the radii of their circular paths?

Smart Achievers · Accepted Answer

(1)

$r_{p} = \frac{\sqrt{2 m_{p} K}}{e B}$ $r_{d} = \frac{\sqrt{2 (2 m_{p}) K}}{e B}$ $r_{a} = \frac{\sqrt{2 (4 m_{p}) K}}{(2 e) B}$

Solution

Q.
A proton, a deuteron and an $α$ particle with the same KE enter in a region of uniform magnetic field, moving at right angles to magnetic field. What is the ratio of the radii of their circular paths

1 $1 : \sqrt{2} : 1$

2 $1 : \sqrt{2} : \sqrt{2}$

3 $\sqrt{2} : 1 : 1$

4 $\sqrt{2} : \sqrt{2} : 1$

Ans.
(1)

$r_{p} = \frac{\sqrt{2 m_{p} K}}{e B}$ $r_{d} = \frac{\sqrt{2 (2 m_{p}) K}}{e B}$ $r_{a} = \frac{\sqrt{2 (4 m_{p}) K}}{(2 e) B}$

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Solution

Q. A proton, a deuteron and an α particle with the same KE enter in a region of uniform magnetic field, moving at right angles to magnetic field. What is the ratio of the radii of their circular paths

1 1:2:1

2 1:2:2

3 2:1:1

4 2:2:1

Ans. (1) rp=2mpKeB rd=2(2mp)KeB ra=2(4mp)K(2e)B