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 B ₀=0.1 k 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)

Step-by-step solution

aligned & x =2 R & x =2 P qB x = 2 2 mqV qB x = 2 ~B 2 mV q aligned Option A For H ⁺ m = 5 3 10⁻²⁷ ~kg x= 2 0.1 2 5 3 10⁻²⁷ 192 1.6 10⁻¹⁹ =4 ~cm Option B For A _ m =144x= 2 0.1 2 144 5 3 10⁻²⁷ 192 1.6 10⁻¹⁹ =48 ~cm Option C for A _m=1 x =4 ~cm & for A _ m =196 x =56 ~cm . so x ₀=4 ~cm & x ₁=56 ~cm x ₁- x ₀=52 ~cm . Option D Minimum width =R for A _ M =196 aligned & R = P qB = 2 mqV qB & R = 1 ~B 2 mV q & w _ = R = 1 0.1 2 196 5 3 10⁻²⁷ 192 1.6 10⁻¹⁹ =28 ~cm aligned