First slide

Force on a charged particle moving in a magnetic field

Question

Which of the following particles will have minimum frequency of revolution when projected with the same velocity perpendicular to a magnetic field ?

Easy

A

$β^{-}$
B

$H^{+}$
C

$H e^{+}$
D

$L i^{+}$

Solution

(4)
$\begin{array}{l} ω = \frac{Q B}{m}, \\ F o r β^{-}, ω_{1} = \frac{e B}{m_{e}} (m_{e} = M a s s o f e l e c t r o n) \\ F o r H^{+}, ω_{2} = \frac{e B}{m_{p}} (m_{p} = M a s s o f p r o t o n) . \\ F o r H e^{+}, ω_{3} = \frac{e_{B}}{4 m_{p}} a n d f o r L i^{+}, ω_{4} = \frac{e_{B}}{6 m_{p}} \\ ∴ ω_{4} < ω_{3} < ω_{2} < ω_{1} . \end{array}$

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