The more massive particle has the greater energy change. Their energy change is

Question

The more massive particle has the greater energy change. Their energy change is the same. The less massive particle has the greater energy change. Suppose electrons in a TV tube are accelerated through a potential difference of 2.00 times 10^4 V from the heated cathode (negative electrode), where they are produced, toward the screen, which also serves as the anode (positive electrode), 25.0 cm away. (a) At what speed would the electrons impact the phosphors on the screen? Assume they accelerate from rest, and ignore relativistic effects. m/s (b) What's the magnitude of the electric field, if it is assumed constant? V/m

Explanation / Answer

(a)

The speed of the electrons will be determined by how energetic they are:

E = (1/2)mv^2 ..............A)

E = qV ..............B)

So qV = (1/2)mv^2

v = sqrt( 2qV/m)

v =  sqrt[( 2 x 1.6 x 10^-19 x 2 x 10^4) / (9.11 x 10^-31)]

v = 8.38 x 10^7 m/s

b)

E = ( 2 x 10^4 v) / (0.25 m)

E = 8 x 10^4 V/m

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