JEE PYQ: Atomic Physics Question 13
Question 13 - 2021 (18 Mar Shift 2)
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:
(1) 1 : 8
(2) 8 : 1
(3) 1 : 4
(4) 4 : 1
Show Answer
Answer: (4)
Solution
$r = \frac{mv}{qB} = \frac{p}{qB} = \frac{\sqrt{2mK}}{qB}$. $\frac{r_p}{r_\alpha} = \frac{p_p}{q_p} \cdot \frac{q_\alpha}{p_\alpha} = 2$. Working through: $\frac{K_p}{K_\alpha} = (1)(4) = 4:1$.
BETA
