A hydrogen isotope separator contains positively ionized hydrogen \( H^1 \), with the isotope of hydrogen, Deuterium \( D^2 \), and other heavy particles, and the ions were released in a potential difference of 200 Volts. The strong magnetic field of 1.4 x 10^{-2} Tesla (out of the page), bends the ions and Deuterium is collected on a separate ionic trap as shown in the figure. (Masses \( M_{H1} = 1.67 x 10^{-27} \, \text{kg}, \, M_{D2} = 2^* M_{H1} \). \( Q(H1, D2) = 1.6 x 10^{-19} \, \text{C} \))What is the diameter of deflection, d for the Deuterium in units of Centi-meter?### Diagram Explanation:The diagram shows an experimental setup where ions are released into a magnetic field. The deflected path is shown with a curved trajectory due to the Lorentz force acting perpendicular to the velocity of the charged particles. The figure illustrates a velocity selector and a detector positioned to capture deflected ions. The path is semi-circular, showing the bending of ions by the magnetic field, with the detector placed at the end of this path. The trajectory forms a part of a circle with radius \( r \) marked, while a symbol \( \Delta V \) represents the potential difference applied across the system.

Given: ∆V=200 V∆V=200 V then Deuterium ions will be accelerated and hence by work energy theorem 12mv2-12mu2 =q∆V Where, m= 2x1.67x10-27 kg q=1.6x10-19C u=0 On substituting the values in the above expression and simplifying as follows, v2=2q∆Vm=2×1.6×10-19×2002×1.67×10-27v2=191.62×108v=13.84×104v=138.4 km/ATherefore, V=138.4 km/A

Answered: A hydrogen isotope separator contains…