Question

A proton, a deuteron and an $r _ { \alpha }$ denote respectively the radii of the trajectories of these particles, then

• A. $r _ { \alpha } = r _ { p } < r _ { d }$
• B. $r _ { \alpha } > r _ { d } > r _ { p }$
• C. $r _ { \alpha } = r _ { d } > r _ { p }$
• D. $r _ { p } = r _ { d } = r _ { \alpha }$

Answer 1

Answer: (A)

$r _ { \alpha } = r _ { p } < r _ { d }$

Answer 2

Given that $K _ { p } = K _ { d } = K _ { \alpha }$= K (say)

We know that m_p = m, m_d = 2m and $q _ { \alpha } = 2 e$

Further$r = \frac { \sqrt { 2 m K } } { q B }$⇒$r _ { d } = \frac { \sqrt { 2 ( 2 m ) K } } { e B } = \sqrt { 2 } r _ { p }$

and $r _ { \alpha } = r _ { p } < r _ { d }$