A proton of mass m and charge +e is moving in a circular orbit in a magnetic field with energy 1 MeV . What should be the energy of α -particle ( mass = 4m and charge = + 2e ), so that it can revolve in the path of the same radius?

Question

A proton of mass m and charge +e is moving in a circular orbit in a magnetic field with energy 1 MeV . What should be the energy of α -particle ( mass = 4m and charge = + 2e ), so that it can revolve in the path of the same radius? (A) 1 MeV (B) 4 MeV (C) 2 MeV (D) 0.5 MeV

Tardigrade Admin · Accepted Answer

r=(√2 m K/q B)⇒ K propto (q2/m)⇒ (Kp/Kα )=((qp/qα ))2× (mα /mp) ⇒ (1/Kα )=((qp/2 qp))2× (4 mp/mp)=1⇒ Kα =1 MeV .

Q. A proton of mass $m$ and charge $+ e$ is moving in a circular orbit in a magnetic field with energy $1 M e V$ . What should be the energy of $α - p a r t i c l e$ ( $ma ss = 4 m$ and $c ha r g e = + 2 e$ ), so that it can revolve in the path of the same radius?

$1 M e V$

$4 M e V$

$2 M e V$

$0.5 M e V$

$r = \frac{2 m K}{qB} \Rightarrow K \propto \frac{q ^{2}}{m} \Rightarrow \frac{K _{p}}{K _{α}} = (\frac{q _{p}}{q _{α}})^{2} \times \frac{m _{α}}{m _{p}}$
$\Rightarrow \frac{1}{K _{α}} = (\frac{q _{p}}{2 q _{p}})^{2} \times \frac{4 m _{p}}{m _{p}} = 1 \Rightarrow K_{α} = 1 M e V$ .

Q. A proton of mass m and charge +e is moving in a circular orbit in a magnetic field with energy 1MeV . What should be the energy of α−particle ( mass=4m and charge=+2e ), so that it can revolve in the path of the same radius?

1MeV

4MeV

2MeV

0.5MeV