What distance must an electron move in a uniform potential gradient 200V/cm in order to gain kinetic energy 3.2∗10−18J?
Given,
Potential Gradient (E) = 200V/cm = 200∗103V/m
Kinetic Energy (Ek)
Charge of Electron (q) = 1.6∗10−19C
Mass of Electron (m) = 9.1∗10−31kg
Distance (S) = ?
We know that,
F=m.a
⇒ a = Fm = q.Em = 1.6∗10−19∗200∗1039.1∗10−31 = 3.5∗1015m/s2
Now,
EK=12m.v2
⇒ v2=2.Ekm = 2∗(3.2∗10−18)(9.1∗10−31) = 7∗1012m/s
Again, to Calculate the distance,
v2=u2+2as [∵ u=0]
S=v22a = 7∗10122∗(3.5∗1015) = 0.001m
Hence,
The required distance is 0.001m.
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