Question

A positive, singly ionized atom of mass number $A_M$ is accelerated from rest by the voltage $192 V$. Thereafter, it enters a rectangular region of width 𝑤 with magnetic field $\bar{B_0} = 0.1𝑘̂$Tesla, as shown in the figure. The ion finally hits a detector at the distance 𝑥 below its starting trajectory. [Given: Mass of neutron/proton =$(5/3) × 10^{−27}$ kg, charge of the electron $= 1.6 × 10^{−19} C.$]

Which of the following option(s) is(are) correct?

• A. The value of 𝑥 for $𝐻^{ +}$ ion is $4 cm$
• B. The value of 𝑥 for an ion with $𝐴M = 144$ is $48 \ cm$
• C. For detecting ions with 1 ≤ 𝐴M ≤ 196, the minimum height $(𝑥_1 − 𝑥_0)$of the detector is 55 cm
• D. The minimum width 𝑤 of the region of the magnetic field for detecting ions with $𝐴_M = 196$ is 56 cm.

Answer 1

Answer: (A), (B)

The value of 𝑥 for $𝐻^{ +}$ ion is $4 cm$

Answer 2

The correct option is (A): The value of 𝑥 for $𝐻^{ +}$ ion is $4 cm$ and (B): The value of 𝑥 for an ion with $𝐴M = 144$ is $48 \ cm$