Formula for kinetic energy of an object:
KE = 0.5mv²
m is the mass and v is the velocity.
Formula for the work done on a charged object by moving it through a potential difference:
W = ΔVq
ΔV is the potential difference and q is the charge of the object.
To find the potential difference needed to decelerate an electron to rest, set the work done on the electron equal to its kinetic energy:
W = KE
Substitute W = ΔVq and KE = 0.5mv²
ΔVq = 0.5mv²
Given values:
q = 1.6×10⁻¹⁹C
m = 9.11×10⁻³¹kg
v = 6.0m/s
Plug in the given values and solve for ΔV
ΔV×1.6×10⁻¹⁹ = 0.5×9.11×10⁻³¹×6.0²
ΔV = 1.02×10⁻¹⁰V
The potential difference is the difference of charge between two points. The potential difference that is needed to stop the given electron is 1.02×10⁻¹⁰ V.
[tex]\Delta V = \dfrac 12\dfrac { mv^2}{q}[/tex]
Where,
[tex]\Delta V[/tex] - Potential difference
[tex]m[/tex]- mass = 9.11×10⁻³¹ kg
[tex]v[/tex] - velocity = 6 m/s
[tex]q[/tex]- charge = 1.6×10⁻¹⁹ C
Put the values in the equation,
[tex]\Delta V = \dfrac 12\times \dfrac { 9.11\times 10^{31}\times 6^2}{ 1.6\times 10^{-19}}\\\\\Delta V = 1.02\times 10^{-10}V[/tex]
Therefore, the potential difference that is needed to stop the given electron is 1.02×10⁻¹⁰ V.
Learn more about Potential differences:
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