A positive, singly ionized atom of mass number 𝐴M is accelerated from rest by the voltage 192 V. Thereafter, it enters a rectangular region of width 𝑤 with magnetic field 𝐵⃗ 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 (𝑥1 − 𝑥0) of the detector is 55 cm. (D) The minimum width 𝑤 of the region of the magnetic field for detecting ions with 𝐴M = 196 is 56 cm.
A positive, singly ionized atom of mass number 𝐴M is accelerated from rest by the voltage 192 V. Thereafter, it enters a rectangular region of width 𝑤 with magnetic field 𝐵⃗ 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 (𝑥1 − 𝑥0) of the detector is 55 cm. (D) The minimum width 𝑤 of the region of the magnetic field for detecting ions with 𝐴M = 196 is 56 cm.