Question

A proton and an $\alpha$ -particle, having kinetic energies $K _{ p }$ and $K _{\alpha}$, respectively, enter into a magnetic field at right angles. The ratio of the radii of trajectory of proton to that of $\alpha$ -particle is 2 : 1 The ratio of $K _{ p }: K _{\alpha}$ is:

• A. 1 : 8
• B. 8 : 1
• C. 1 : 4
• D. 4 : 1

Answer 1

Answer: (D)

$r =\frac{ mv }{ qB }=\frac{ p }{ qB }$
$ \frac{ m _{\alpha}}{ m _{ p }}=4$
$\frac{ r _{ p }}{ r _{a}}=\frac{ p _{ p }}{ q _{ p }} \frac{ q _{\alpha}}{ p _{\alpha}}=\frac{2}{1}$
$\frac{ p _{ p }}{ p _{\alpha}}=\frac{2 q _{ p }}{ q _{\alpha}}=2\left(\frac{1}{2}\right)$
$\frac{ p _{ q }}{ p _{a}}=1$
$\frac{ K _{ p }}{ K _{\alpha}}=\frac{ p _{ p }^{2}}{ p _{\alpha}^{2}} \frac{ m _{\alpha}}{ m _{ p }}=(1)$ (4)