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Darina [25.2K]
2 years ago
6

Two electrons are at rest and separated by a distance of 4.32 × 10-10 m. When they are released they accelerate away from each o

ther. What is the speed of either electron when their separation has increased by a factor of 4.10?
Physics
1 answer:
sasho [114]2 years ago
5 0

Answer:

Speed of electron when their separation increased by a factor of 4.10 is 9.41 x 10⁵ m/s .

Explanation:

The electric potential energy is given by the relation :

U = \frac{kq_{1}q_{2}  }{r}

Here q₁ and q₂ are the two charge particles and r is the distance between them and k is electric constant.

In this case, there are two electrons which are separated by the distance 4.32 x 10⁻¹⁰ m.

Let e be the electron charge and r₁ be the distance between them. Then, the initial electric potential energy is :

U_{1}  = \frac{ke^{2}   }{r_{1} }

Now, the distance between the electrons increases by the factor of 4.10. Let r₂ be the new distance between them i.e. r₂ = 4.10 r₁.

Thus, the new electric potential energy is :

U_{2}  = \frac{ke^{2}   }{r_{2} }=\frac{ke^{2}   }{4.10r_{1} }

Applying law of conservation of energy :

ΔU  = ΔK

Here ΔU is change in electric potential energy and ΔK is change in kinetic energy.

( U₁  - U₂ ) = ( K₂ - K₁ )

Here K₂ and K₁ are initial and final kinetic energy of electron.

Since, the electron initially is at rest, so its initial kinetic energy is zero. Thus, the above equation becomes:

K₂ = U₁ - U₂

\frac{1}{2}mv^{2}=\frac{ke^{2}   }{r_{1} }- \frac{ke^{2}   }{4.10r_{1} }

Here m and v are the mass and final speed of electron respectively.

v^{2}=\frac{2}{m} \frac{ke^{2}   }{r_{1} }(1- \frac{1  }{4.10 })

Substitute 9.1 x 10⁻³¹ kg for m, 9 x 10⁹ N m² C⁻² for k, 1.6 x 10⁻¹⁹ C for e and 4.32 x 10⁻¹⁰ m for r₁ in the above equation.

v^{2}=\frac{2}{9.1\times10^{-31} } \frac{9\times10^{9}\times(1.6\times10^{-19})^{2}   }{4.32\times10^{-10} }(1- \frac{1  }{4.10 })

v^{2}=8.86\times10^{11}

v = 9.41 x 10⁵ m/s

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