It is not possible to see very small objects, such as viruses, using an ordinary

Question

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 i. As it passes through the region x = 0 to x = d, the electron experiences acceleration a = a_x i + a_y j, where a_x and a_y are constants. For the case v_i = 1.84 times 10^7 m/s, a_x = 7.26 times 10^14 m/s^2, and a_y = 1.77 times 10^15 m/s^2, determine the following at x = d = 0.0100 m. (a) the position of the electron Y_f = (b) the velocity of the electron V_f = (c) the speed of the electron |V_f| = (d) the direction of travel of the electron (i.e. the angle between its velocity and the x axis) theta = 2.9 theta

Explanation / Answer

ax= 7.26e14 m/s2

ay=1.77e15 m/s2

a= sqrt{(7.26e14)^2+(1.77e15)^2}

a = 19.13e14 m/s2

Now

a) Time taken by electron to cover d=0.01. m

d=ut +1/2 at2

0.01= 1.84e7t +0.5 x19.13e14

0.01 = 1.84e7t+ 9.565e14t2

t=5.289e-10 s

a) position of electron rf = ri +vyt + 1/2 ayt2

=0 + 1/2 {(1.77e15)(5.289e-10)^2}

=24.76e-5 m

b)

Vf = vi + at

=1.84e7i+( 7.26e14i +1.77e15j )5.289e-10

=1.8783e7 i + 9.362 e5 j m/s

c) speed of electron v = sqrt{(1.8783e7)^2 + (9.362e5)^2} =132.167 m/s

d) theta = arctan 0.049842943 = 2.85 degree or 2.9 degree

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