Question

A proton and an alpha particle enter a magnetic field with same kinetic energy.then the ratio of radius described by them

Answer 1

R = mv/qB = √(2mKe)/qB

theyve same kinetic energy then
radius is in ratio of root of their mass and charge as per above formula

Rp:Rα = 1:1

Answer 2

answer : 1 : 1

radius described by charged particle in magnetic field is given by, $r=\frac{mv}{qB}$ or, $\frac{P}{qB}$

where P is linear momentum of charged particle, q is charge on it and B is magnitude of magnetic field .

we know, kinetic energy , K = P²/2m

so, P = √{2Km}

now r = √{2Km}/qB

if K and B are constant then, r is directly proportional to square root of m and inversely proportional to q.

or, $\frac{r_1}{r_2}=\sqrt{\frac{m_1}{m_2}}\frac{q_2}{q_1}$

mass of proton, $m_1=1u$

mass of alpha particle, $m_2=4u$

charge on proton, $q_1=1e$

charge on alpha particle, $q_2=2e$

so, ratio of radius = √(1u/4u) × (2e/1e) = 1

hence, ratio of radius described by them is 1 : 1