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An electron with initial velocity 1'0 = 1.5 X 105 m/s enters a region 1.2 long where it is electrically accelerated (see Fig). It emerges with a velocity v = 5.8 X 106 m/s. What was its acceleration, assumed constant? (Such a process occurs in the electron gun in a cathode-ray tube, used in television receivers and computer monitors.)

An electron with initial velocity 1'0 = 1.5 X 105 m/s enters a region 1.2 long where it is electrically accelerated (see Fig). It emerges with a velocity v = 5.8 X 106 m/s.
What was its acceleration, assumed constant? (Such a process occurs in the electron gun in a cathode-ray tube, used in television receivers and computer monitors.)

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
6 years ago
Initial velocity of electrons, v0 = 1.5 x 105.
Final velocity of electrons, v = 5.8 x 106.
Length of tube, x = 1.2 cm.
Let us assume that the constant acceleration of the electrons is a and it takes t seconds for the jet to reach the final speed v.
From the equation of kinematics, we have
232-614_1.PNG
We can solve for acceleration from the above two equation by eliminating the variable t.
From the second equation, the time t is given as:

232-1409_2.PNGTherefore the acceleration of the electrons is1.4 x 1015 m/s2.
232-1638_3.PNG
Therefore the acceleration of the electrons is1.4 x 1015 m/s2.

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