A proton and a deuteron both having the same kinetic energy, enter perpendicularly into a uniform magnetic field B. For motion of proton and deuteron on circular path of radius rP and rd respectively, the correct statement is

Question

A proton and a deuteron both having the same kinetic energy, enter perpendicularly into a uniform magnetic field B. For motion of proton and deuteron on circular path of radius rP and rd respectively, the correct statement is (A) rd=rP √2 (B) rd (rP/√2) (C) rd=rP (D) rd=2 rP

Tardigrade Admin · Accepted Answer

Radius of circular path r=(m v/q B)...(i) and kinetic energy K E=(1/2) m v2 or v=√(2 K E/m) putting the value of v in Eq. (i) r=(m/q B) √(2 K E/m)=(√2 m K E/q B) ldots (ii) For proton ( 1 H1) and deuteron ( 1 H2) electronic charge are same and both have same kinetic energy. ∴ By Eq. (ii) r propto √m or (rd/rp)=√(md/mp) ∵ md=2 mp ∴ (rd/rp)=√(2 mp/mp) ⇒ rd=√2 rp

Q. A proton and a deuteron both having the same kinetic energy, enter perpendicularly into a uniform magnetic field $B$ . For motion of proton and deuteron on circular path of radius $r_{P}$ and $r_{d}$ respectively, the correct statement is

$r_{d} = r_{P} 2$

$r_{d} \frac{r _{P}}{2}$

$r_{d} = r_{P}$

$r_{d} = 2 r_{P}$

Q. A proton and a deuteron both having the same kinetic energy, enter perpendicularly into a uniform magnetic field B. For motion of proton and deuteron on circular path of radius rP​ and rd​ respectively, the correct statement is

rd​=rP​2​

rd​2​rP​​

rd​=rP​

rd​=2rP​

Q. A proton and a deuteron both having the same kinetic energy, enter perpendicularly into a uniform magnetic field $B$ . For motion of proton and deuteron on circular path of radius $r_{P}$ and $r_{d}$ respectively, the correct statement is

$r_{d} = r_{P} 2$

$r_{d} \frac{r _{P}}{2}$

$r_{d} = r_{P}$

$r_{d} = 2 r_{P}$