A proton and an α- particle enter in a uniform magnetic field perpendicularly with same speed. The ratio of time periods of both particle ((Tp/Tα)) will be

Question

A proton and an α- particle enter in a uniform magnetic field perpendicularly with same speed. The ratio of time periods of both particle ((Tp/Tα)) will be (A) 1: 2 (B) 1:3 (C) 2:1 (D) 3:1

Tardigrade Admin · Accepted Answer

The time period of revolution of a charged particle in a magnetic field is

T = \frac{2 πm}{Bq}

For proton,

m_{p} = m, q_{p} = q

;

∴ T_{p} = \frac{2 πm}{Bq}

Now, for

α

-particle,

m_{α} = 4 m

,

q_{α} = 2 q

∴ T_{α} = \frac{2 π ( 4 m )}{B ( 2 q )} = 2 (\frac{2 πm}{Bq})

\Rightarrow \frac{T _{p}}{T _{α}} = \frac{1}{2}

Q. A proton and an $α$ - particle enter in a uniform magnetic field perpendicularly with same speed. The ratio of time periods of both particle $(\frac{T _{p}}{T _{α}})$ will be

$1 : 2$

$1 : 3$

$2 : 1$

$3 : 1$

Q. A proton and an α- particle enter in a uniform magnetic field perpendicularly with same speed. The ratio of time periods of both particle (Tα​Tp​​) will be

1:2

1:3

2:1

3:1

The time period of revolution of a charged particle in a magnetic field is T=Bq2πm​ For proton, mp​=m,qp​=q; ∴Tp​=Bq2πm​ Now, for α -particle, mα​=4m, qα​=2q ∴Tα​=B(2q)2π(4m)​=2(Bq2πm​) ⇒Tα​Tp​​=21​

Q. A proton and an $α$ - particle enter in a uniform magnetic field perpendicularly with same speed. The ratio of time periods of both particle $(\frac{T _{p}}{T _{α}})$ will be

$1 : 2$

$1 : 3$

$2 : 1$

$3 : 1$