Question

Four charge particles $H{e}^{++},$ proton, deutron and $L{i}^{++}$ enters a region of uniform magnetic field and moves in circular path of different radius. List I gives above four paticles while List II gives magnitude of some quantity.
$\begin{array}{cc}\text{List I}& \text{List II}\\ \text{I -}H{e}^{++}& \text{P)}1\\ \text{II -}\text{Proton}& \text{Q)}2\\ \text{III -}\text{deutron}& \text{R)}\frac{1}{\sqrt{2}}\\ \text{IV)}L{i}^{++}& \text{S)}\sqrt{2}\\ & \text{T)}\frac{\sqrt{7}}{2}\\ & \text{U)}\frac{1}{2}\end{array}$
If momentum of all four particles is same then correct match for radius of four particles in units of radius of proton is

• A. I - P, II - P, III - U, IV - U
• B. I - U, II - P, III - P, IV - T
• C. I - U, II - P, III - Q - IV - T
• D. I - U, II - P, III - P, IV - U

Answer 1

The correct option is D I - U, II - P, III - P, IV - U

$I\to U,II\to P,III\to P,IV\to U$
Since $R=\frac{mv}{qB}=\frac{p}{qB}{R}_P=\frac{P}{eB}=R_0\left(let\right)$
$R_{H{e}^{++}}\frac{P}{2eB}=\frac{R_0}{2}{R}_d=\frac{P}{eB}=R_0$
$R_{L{i}^{++}}=\frac{P}{2eB}=\frac{R_0}{2}$
Here P is momentum