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

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 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 ) × 1 0 − 27 kg , charge of the electron = 1.6 × 1 0 − 19 C .] Which of the following option(s) is(are) correct?

TestHub · Accepted Answer

​ x = 2 R ⇒ x = 2 qB P ​ ⇒ x = qB 2 2 mqV ​ ​ ⇒ x = B 2 ​ q 2 mV ​ ​ ​ Option A For H + → m = 3 5 ​ × 1 0 − 27 kg ∴ x = 0.1 2 ​ 1.6 × 1 0 − 19 2 × 3 5 ​ × 1 0 − 27 × 192 ​ ​ = 4 cm Option B For A m ​ = 144 x = 0.1 2 ​ 1.6 × 1 0 − 19 2 × 144 × 3 5 ​ × 1 0 − 27 × 192 ​ ​ = 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 ​ R = qB P ​ = qB 2 mqV ​ ​ R = B 1 ​ q 2 mV ​ ​ w m i n ​ = R = 0.1 1 ​ 1.6 × 1 0 − 19 2 × 196 × 3 5 ​ × 1 0 − 27 × 192 ​ ​ = 28 cm ​

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Options:(select one or more)

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