Question 171: Magnetism and Matter

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 :

Accepted Answer

Radius, $$r = {{mv} \over {qB}} = {{\sqrt {2mK} } \over {qB}}$$
$$ \Rightarrow K = {{{r^2}{q^2}{B^2}} \over {2m}}$$
$$ 	herefore $$ $${{{K_p}} \over {{K_\alpha }}} = {\left( {{{{r_p}} \over {{r_\alpha }}}} ight)^2} 	imes {\left( {{{{q_p}} \over {{q_\alpha }}}} ight)^2} 	imes {{{m_\alpha }} \over {{m_p}}}$$
$$ = {\left( {{2 \over 1}} ight)^2} 	imes {\left( {{1 \over 2}} ight)^2} 	imes 4$$
$$ = 4$$

Answer

8 : 1

Answer

4 : 1

Answer

1 : 8

Answer

1 : 4

Magnetism and Matter

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 :

Choose the correct answer: