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NeX [460]
3 years ago
15

Consider an electron placed in a region of space in which the electric potential spatially. The electron is placed at a point wh

ere the potential is -1000V relative to ground, and it is observed to accelerate to a point where the potential is -500V relative to ground. How fast is the electron moving at that point, assuming nothing else impacts the electron's motion
Chemistry
1 answer:
loris [4]3 years ago
5 0

Answer:

1.33\cdot 10^7 m/s

Explanation:

For a charged particle accelerated by an electric field, the kinetic energy gained by the particle is equal to the decrease in electric potential energy of the particle; therefore:

K_f-K_i = -q\Delta V

where

K_f is the final kinetic energy

K_i is the initial kinetic energy

q is the charge of the particle

\Delta V is the potential difference

In this problem,

q=-1.6\cdot 10^{-19}C is the charge of the electron

\Delta V=-500 V-(-1000 V)=500 V

The electron starts from rest, so its initial kinetic energy is

K_i=0

Therefore,

K_f=-(-1.6\cdot 10^{-19})(500)=8\cdot 10^{-17}J

We can write the final kinetic energy of the electron as

K_f=\frac{1}{2}mv^2

where

m=9.11\cdot 10^{-31} kg is the electron mass

v is the final speed

And solving for v,

v=\sqrt{\frac{2K_f}{m}}=\sqrt{\frac{2(8\cdot 10^{-17})}{9.11\cdot 10^{-31}}}=1.33\cdot 10^7 m/s

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