Question

Problem 5 (25pts). We want to build a system which is meant to filter H from H2 ions. Below we have a schematic for the proposed system. Initially the ions are at rest and are accelerated horizontally by a 10 kV potential difference. They pass through an opening into another ion accelerator which has a vertical potential difference also of 10 kV (see schematic for the proposed syastem They pass through an openinu (a) What are the exit coordinates of H from accelerator 2? (b) What are the exit coordinates of H2 from accelerator 2? (c) Is the design proposed for the filter eflicient? Remember that Fmã 10 kv o V Ha 1m H. starting position 20cm 10 kv 1m 0.5m

We want to build a system which is meant to filter H- from H2- ions. Below we have a schematic for the proposed system. Initially the ions are at rest and are accelerated horizontally by a 10 kV potential difference. They pass through an opening into another ion accelerator which has a vertical potential difference also of 10 kV (see schematic).

(a) What are the exit coordinates of H- from accelerator 2?

(b) What are the exit coordinates of H2- from accelerator 2?

(c) Is the design proposed for the filter efficient? Remember that ~

Please provide an explanation for the solution.

Answer 1

Horizontally speed of H^- at opening v_1x = squareroot 2eV/m = squareroot 2 times 1.6 times 10^-19 times 10 times 10^3/1.67 times 10^-27 m/s v_1x = 1.38 times 10^6 m/s Acceleration a_1y = F/m = eV/mL Therefore a_1y = 1.6 times 10^-19 times 10 times 10^3/1.67 times 10^-27 times 1 = 9.58 times 10^11 m/s^2 time taken to travel x = 1m, is t_1 = 1/1.38 times 10^6 S Therefore y-cordinate, y_1 = y_0 1/2a_1t_1^2 = 0.20 + 1/2 times 9.58 times 10^11 times (1/1.38 times 10^6) Therefore y_1 = 0.20 + 0.25 = 0.45m Therefore x_1 = 1m, y_1 = 0.45m for H_2^- , m_2 = 2 times 1.67 times 10^-27kg Therefore v_2x = squareroot 2 times 1.6 times 10^-19 times 10 times 10^3/2 times 1.67 times 10^-27 = 9.788 times 10^5 m/s a_2y = eV/2ml = 1.6 times 10^-19 times 10 times 10^3/2 times 1.67 times 10^-27 times 1 m/s^2 = 4.79 times 10^11 m/s^2