I am really lost on this one.... It is not possible to see very small objects, s

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I am really lost on this one....

It is not possible to see very small objects, such as viruses, using an ordinary light microscope. An electron microscope can view such objects using an electron beam instead of a light beam. Electron microscopy has proved invaluable for investigations of viruses, cell membranes and subcellular structures, bacterial surfaces, visual receptors, chloroplasts, and the contractile properties of muscles. The "lenses" of an electron microscope consist of electric and magnetic fields that control the electron beam. As an example of the manipulation of an electron beam, consider an electron traveling away from the origin along the x axis in the xy plane with initial velocity V_1 = v,i. As it passes through the region x = 0 to x = d, the electron experiences acceleration a = a_x= + a_yj, where a_x and a_y are constants. For the case v, = 1.60 x 10^7 m/s, ax = 8.29 x 10^14 m/s^2, and a_y = 1.54 x 10^15 m/s^2, determine the following at x = d = 0.0100 m. (a) the position of the electron (b) the velocity of the electron (c) the speed of the electron Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error, m/s (d) the direction of travel of the electron (i.e. the angle between its velocity and the x axis) Teta =

Explanation / Answer

a) Final speed in x-direction, vfx = (vix2 + 2axd)1/2 = [(1.60 * 107)2 + (2 * 8.29 * 1014 * 0.01)]1/2 = 1.651 * 107 m/s

Time taken, t = (vfx - vix)/ax = (1.651 - 1.60) * 107 / (8.29 * 1014) = 6.152 * 10-10 s

So, yf = viyt + ayt2/2 = 0 + [1.54 * 1015 * (6.152 * 10-10)2 / 2] = 2.914 * 10-4 m

b) vfy = viy + ayt = 0 + [1.54 * 1015 * (6.152 * 10-10)] = 9.474 * 105 m/s

So, vf = vfxi + vfyj = (1.651 * 107 m/s)i + (9.474 * 105 m/s)j = 105 * (165.1i + 9.474j)

c) |vf| = (165.12 + 9.4742)1/2 * 105 = 1.654 * 107 m/s

d) Angle between the velocity and the x-axis, = tan-1(vfy / vfx) = tan-1[(9.474 / 165.1] = 3.284o

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